-
question_answer1)
A square is inscribed in the circle\[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\], whose sides are parallel to the coordinate axes. One vertex of the square is [IIT 1980; DCE 2001]
A)
\[(1+\sqrt{2},\ -2)\] done
clear
B)
\[(1-\sqrt{2},\ -2)\] done
clear
C)
\[(1,\ -2+\sqrt{2})\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer2)
If the line \[x+2by+7=0\] is a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-6x+2y=0\], then \[b=\] [MP PET 1991]
A)
3 done
clear
B)
- 5 done
clear
C)
- 1 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer3)
For all values of \[\theta \], the locus of the point of intersection of the lines \[x\cos \theta +y\sin \theta =a\] and \[x\sin \theta -y\cos \theta =b\] is
A)
An ellipse done
clear
B)
A circle done
clear
C)
A parabola done
clear
D)
A hyperbola done
clear
View Solution play_arrow
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question_answer4)
If a circle whose centre is (1, ?3) touches the line \[3x-4y-5=0\], then the radius of the circle is
A)
2 done
clear
B)
4 done
clear
C)
\[\frac{5}{2}\] done
clear
D)
\[\frac{7}{2}\] done
clear
View Solution play_arrow
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question_answer5)
If the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] touches x-axis, then
A)
\[g=f\] done
clear
B)
\[{{g}^{2}}=c\] done
clear
C)
\[{{f}^{2}}=c\] done
clear
D)
\[{{g}^{2}}+{{f}^{2}}=c\] done
clear
View Solution play_arrow
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question_answer6)
The equation of the circle which touches both the axes and whose radius is a, is [MP PET 1984]
A)
\[{{x}^{2}}+{{y}^{2}}-2ax-2ay+{{a}^{2}}=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+ax+ay-{{a}^{2}}=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2ax+2ay-{{a}^{2}}=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-ax-ay+{{a}^{2}}=0\] done
clear
View Solution play_arrow
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question_answer7)
The area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) is [MNR 1982; IIT 1980; Karnataka CET 1999; MP PET 2002; DCE 2000; Pb. CET 2002]
A)
\[5\pi \] done
clear
B)
\[10\pi \] done
clear
C)
\[25\pi \] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer8)
The centres of the circles \[{{x}^{2}}+{{y}^{2}}=1\], \[{{x}^{2}}+{{y}^{2}}+6x-2y=1\] and \[{{x}^{2}}+{{y}^{2}}-12x+4y=1\] are [MP PET 1986]
A)
Same done
clear
B)
Collinear done
clear
C)
Non-collinear done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer9)
If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is [MNR 1975]
A)
\[(a,\ b)\] done
clear
B)
\[(b,\ a)\] done
clear
C)
\[\left( \frac{a}{2},\ \frac{b}{2} \right)\] done
clear
D)
\[\left( \frac{b}{2},\ -\frac{a}{2} \right)\] done
clear
View Solution play_arrow
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question_answer10)
The equation of the circle whose centre is (1, ?3) and which touches the line \[2x-y-4=0\] is
A)
\[5{{x}^{2}}+5{{y}^{2}}-10x+30y+49=0\] done
clear
B)
\[5{{x}^{2}}+5{{y}^{2}}+10x-30y+49=0\] done
clear
C)
\[5{{x}^{2}}+5{{y}^{2}}-10x+30y-49=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
The circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] touches [MP PET 1988]
A)
x-axis done
clear
B)
y-axis done
clear
C)
x-axis and y-axis done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer12)
The equation of the circle which touches both axes and whose centre is \[({{x}_{1}},\ {{y}_{1}})\] is [MP PET 1988]
A)
\[{{x}^{2}}+{{y}^{2}}+2{{x}_{1}}(x+y)+x_{1}^{2}=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2{{x}_{1}}(x+y)+x_{1}^{2}=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x{{x}_{1}}+2y{{y}_{1}}=0\] done
clear
View Solution play_arrow
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question_answer13)
The equation of the circle whose radius is 5 and which touches the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\] externally at the point (5, 5), is [Pb. CET 2003; IIT 1979]
A)
\[{{x}^{2}}+{{y}^{2}}-18x-16y-120=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-18x-16y+120=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+18x+16y-120=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+18x-16y+120=0\] done
clear
View Solution play_arrow
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question_answer14)
The lines \[2x-3y=5\] and \[3x-4y=7\] are the diameters of a circle of area 154 square units. The equation of the circle is [IIT 1989; AIEEE 2003; Kerala (Engg.) 2005]
A)
\[{{x}^{2}}+{{y}^{2}}+2x-2y=62\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x+2y=47\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x-2y=47\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2x+2y=62\] done
clear
View Solution play_arrow
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question_answer15)
A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. The radius of the circle is [MP PET 1992]
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer16)
The number of circle having radius 5 and passing through the points (? 2, 0) and (4, 0) is
A)
One done
clear
B)
Two done
clear
C)
Four done
clear
D)
Infinite done
clear
View Solution play_arrow
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question_answer17)
The equation of the circle which touches x-axis and whose centre is (1, 2), is [MP PET 1984]
A)
\[{{x}^{2}}+{{y}^{2}}-2x+4y+1=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x+4y+1=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+4x+2y+4=0\] done
clear
View Solution play_arrow
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question_answer18)
The locus of the centre of the circle which cuts off intercepts of length \[2a\] and \[2b\] from x-axis and y-axis respectively, is
A)
\[x+y=a+b\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] done
clear
C)
\[{{x}^{2}}-{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done
clear
View Solution play_arrow
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question_answer19)
If the lines \[3x-4y+4=0\] and \[6x-8y-7=0\] are tangents to a circle, then the radius of the circle is [IIT 1984; MP PET 1994, 2002; RPET 1995, 97; Kurukshetra CEE 1998]
A)
3/2 done
clear
B)
3/4 done
clear
C)
1/10 done
clear
D)
1/20 done
clear
View Solution play_arrow
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question_answer20)
If the radius of the circle \[{{x}^{2}}+{{y}^{2}}\] \[-18x+12y+k=0\] be 11, then \[k=\] [MP PET 1987]
A)
347 done
clear
B)
4 done
clear
C)
\[-\,4\] done
clear
D)
49 done
clear
View Solution play_arrow
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question_answer21)
Centre of circle \[(x-{{x}_{1}})(x-{{x}_{2}})\] \[+(y-{{y}_{1}})(y-{{y}_{2}})\] \[=0\] is
A)
\[\left( \frac{{{x}_{1}}+{{y}_{1}}}{2},\ \frac{{{x}_{2}}+{{y}_{2}}}{2} \right)\] done
clear
B)
\[\left( \frac{{{x}_{1}}-{{y}_{1}}}{2},\ \frac{{{x}_{2}}-{{y}_{2}}}{2} \right)\] done
clear
C)
\[\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\ \frac{{{y}_{1}}+{{y}_{2}}}{2} \right)\] done
clear
D)
\[\left( \frac{{{x}_{1}}-{{x}_{2}}}{2},\ \frac{{{y}_{1}}-{{y}_{2}}}{2} \right)\] done
clear
View Solution play_arrow
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question_answer22)
ABC is a triangle in which angle C is a right angle. If the coordinates of A and B be (?3, 4) and (3,?4) respectively, then the equation of the circumcircle of triangle ABC is
A)
\[{{x}^{2}}+{{y}^{2}}-6x+8y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=25\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-3x+4y+5=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer23)
The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is [RPET 1991; MP PET 1987, 89]
A)
\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer24)
The number of circles touching the line \[y-x=0\] and the y-axis is
A)
Zero done
clear
B)
One done
clear
C)
Two done
clear
D)
Infinite done
clear
View Solution play_arrow
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question_answer25)
The equation of the circle passing through the point \[(-1,\ -3)\] and touching the line \[4x+3y-12=0\] at the point (3, 0), is
A)
\[{{x}^{2}}+{{y}^{2}}-2x+3y-3=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+2x-3y-5=0\] done
clear
C)
\[2{{x}^{2}}+2{{y}^{2}}-2x+5y-8=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer26)
If the vertices of a triangle be \[(2,\ -2)\], \[(-1,\ -1)\] and (5, 2), then the equation of its circumcircle is
A)
\[{{x}^{2}}+{{y}^{2}}+3x+3y+8=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-3x-3y-8=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-3x+3y+8=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer27)
The equation of a circle which touches both axes and the line \[3x-4y+8=0\] and whose centre lies in the third quadrant is [MP PET 1986]
A)
\[{{x}^{2}}+{{y}^{2}}-4x+4y-4=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x+4y+4=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+4x+4y+4=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-4y-4=0\] done
clear
View Solution play_arrow
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question_answer28)
If one end of a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y+11=0\]be (3, 4), then the other end is [MP PET 1986; BIT Ranchi 1991]
A)
(0, 0) done
clear
B)
(1, 1) done
clear
C)
(1, 2) done
clear
D)
(2, 1) done
clear
View Solution play_arrow
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question_answer29)
If the equation \[p{{x}^{2}}+(2-q)xy+3{{y}^{2}}\] \[-6qx+30y+6q=0\] represents a circle, then the values of p and q are
A)
3, 1 done
clear
B)
2, 2 done
clear
C)
3, 2 done
clear
D)
3, 4 done
clear
View Solution play_arrow
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question_answer30)
The equation of the circle passing through the origin and cutting intercepts of length 3 and 4 units from the positive axes, is
A)
\[{{x}^{2}}+{{y}^{2}}+6x+8y+1=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-6x-8y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+3x+4y=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-3x-4y=0\] done
clear
View Solution play_arrow
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question_answer31)
Circle \[{{x}^{2}}+{{y}^{2}}+6y=0\]touches
A)
y-axis at the origin done
clear
B)
x-axis at the origin done
clear
C)
x-axis at the point (3, 0) done
clear
D)
The line \[y+3=0\] done
clear
View Solution play_arrow
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question_answer32)
The circle represented by the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] will be a point circle, if
A)
\[{{g}^{2}}+{{f}^{2}}=c\] done
clear
B)
\[{{g}^{2}}+{{f}^{2}}>c\] done
clear
C)
\[{{g}^{2}}+{{f}^{2}}+c=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer33)
The equation of the circle having centre \[(1,\ -2)\] and passing through the point of intersection of lines \[3x+y=14\], \[2x+5y=18\] is [MP PET 1990]
A)
\[{{x}^{2}}+{{y}^{2}}-2x+4y-20=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x-4y-20=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x+4y-20=0\] done
clear
View Solution play_arrow
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question_answer34)
For the circle \[{{x}^{2}}+{{y}^{2}}+6x-8y+9=0\], which of the following statements is true
A)
Circle passes through the point \[(-3,\ 4)\] done
clear
B)
Circle touches x-axis done
clear
C)
Circle touches y-axis done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer35)
Equation of the circle which touches the lines \[x=0,\ y=0\] and \[3x+4y=4\] is [MP PET 1991]
A)
\[{{x}^{2}}-4x+{{y}^{2}}+4y+4=0\] done
clear
B)
\[{{x}^{2}}-4x+{{y}^{2}}-4y+4=0\] done
clear
C)
\[{{x}^{2}}+4x+{{y}^{2}}+4y+4=0\] done
clear
D)
\[{{x}^{2}}+4x+{{y}^{2}}-4y+4=0\] done
clear
View Solution play_arrow
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question_answer36)
For the line \[3x+2y=12\] and the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y+3=0\], which of the following statements is true
A)
Line is a tangent to the circle done
clear
B)
Line is a chord of the circle done
clear
C)
Line is a diameter of the circle done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer37)
The locus of the centre of the circle which cuts a chord of length 2a from the positive x-axis and passes through a point on positive y-axis distant b from the origin is
A)
\[{{x}^{2}}+2by={{b}^{2}}+{{a}^{2}}\] done
clear
B)
\[{{x}^{2}}-2by={{b}^{2}}+{{a}^{2}}\] done
clear
C)
\[{{x}^{2}}+2by={{a}^{2}}-{{b}^{2}}\] done
clear
D)
\[{{x}^{2}}-2by={{b}^{2}}-{{a}^{2}}\] done
clear
View Solution play_arrow
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question_answer38)
The equation of circle passing through (4, 5) and having the centre at (2, 2), is [MNR 1986; MP PET 1984]
A)
\[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x=13\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\] done
clear
View Solution play_arrow
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question_answer39)
A circle touches x-axis and cuts off a chord of length 2l from y-axis. The locus of the centre of the circle is
A)
A straight line done
clear
B)
A circle done
clear
C)
An ellipse done
clear
D)
A hyperbola done
clear
View Solution play_arrow
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question_answer40)
Radius of circle \[(x-5)(x-1)+(y-7)(y-4)=0\] is
A)
3 done
clear
B)
4 done
clear
C)
5/2 done
clear
D)
7/2 done
clear
View Solution play_arrow
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question_answer41)
The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line \[y-4x+3=0\], is [RPET 1985; MP PET 1989]
A)
\[{{x}^{2}}+{{y}^{2}}+4x-10y+25=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x-10y+16=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-14y+8=0\] done
clear
View Solution play_arrow
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question_answer42)
The equation of the circle with centre at (1, ?2) and passing through the centre of the given circle \[{{x}^{2}}+{{y}^{2}}+2y-3=0\], is
A)
\[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x+4y-3=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x-4y-3=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+2x-4y+3=0\] done
clear
View Solution play_arrow
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question_answer43)
The equation of the circle concentric with the circle \[{{x}^{2}}+{{y}^{2}}+8x+10y-7=0\] and passing through the centre of the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y=0\] is
A)
\[{{x}^{2}}+{{y}^{2}}+8x+10y+59=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+8x+10y-59=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x-6y+87=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-6y-87=0\] done
clear
View Solution play_arrow
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question_answer44)
The equation of the circle passing through the points (0, 0), (0, b) and (a, b) is [AMU 1978]
A)
\[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-ax+by=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+ax-by=0\] done
clear
View Solution play_arrow
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question_answer45)
The equation \[a{{x}^{2}}+b{{y}^{2}}+2hxy+2gx+2fy+c=0\] will represent a circle, if [MNR 1979; MP PET 1988; RPET 1997, 2003]
A)
\[a=b=0\] and \[c=0\] done
clear
B)
\[f=g\] and \[h=0\] done
clear
C)
\[a=b\ne 0\] and \[h=0\] done
clear
D)
\[f=g\] and \[c=0\] done
clear
View Solution play_arrow
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question_answer46)
The equations of the circles touching both the axes and passing through the point (1, 2) are
A)
\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0,\ {{x}^{2}}+{{y}^{2}}-10x-10y+25=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0,\ {{x}^{2}}+{{y}^{2}}-10x-10y-25=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x+2y+1=0,\ {{x}^{2}}+{{y}^{2}}+10x+10y+25=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer47)
Which of the following line is a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-6x-8y-9=0\]
A)
\[3x-4y=0\] done
clear
B)
\[4x-3y=9\] done
clear
C)
\[x+y=7\] done
clear
D)
\[x-y=1\] done
clear
View Solution play_arrow
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question_answer48)
A circle is concentric with the circle \[{{x}^{2}}+{{y}^{2}}-6x+12y+15=0\] and has area double of its area. The equation of the circle is
A)
\[{{x}^{2}}+{{y}^{2}}-6x+12y-15=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-6x+12y+15=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-6x+12y+45=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer49)
If the radius of the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] be r, then it will touch both the axes, if
A)
\[g=f=r\] done
clear
B)
\[g=f=c=r\] done
clear
C)
\[g=f=\sqrt{c}=r\] done
clear
D)
\[g=f\] and \[{{c}^{2}}=r\] done
clear
View Solution play_arrow
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question_answer50)
The equation of the circle with centre on the x-axis, radius 4 and passing through the origin, is
A)
\[{{x}^{2}}+{{y}^{2}}+4x=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-8y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}\pm 8x=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+8y=0\] done
clear
View Solution play_arrow
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question_answer51)
The equation of the circle passing through the point (2, 1) and touching y-axis at the origin is
A)
\[{{x}^{2}}+{{y}^{2}}-5x=0\] done
clear
B)
\[2{{x}^{2}}+2{{y}^{2}}-5x=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+5x=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer52)
The equation of the circle which passes through the origin and cuts off intercepts of 2 units length from negative coordinate axes, is
A)
\[{{x}^{2}}+{{y}^{2}}-2x+2y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+2x-2y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x+2y=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] done
clear
View Solution play_arrow
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question_answer53)
For the circle \[{{x}^{2}}+{{y}^{2}}+3x+3y=0\], which of the following relations is true
A)
Centre lies on x-axis done
clear
B)
Centre lies on y-axis done
clear
C)
Centre is at origin done
clear
D)
Circle passes through origin done
clear
View Solution play_arrow
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question_answer54)
The equation of the circle with centre on x-axis, radius 5 and passing through the point (2, 3), is
A)
\[{{x}^{2}}+{{y}^{2}}+4x-21=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+4x+21=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x-21=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+5x-21=0\] done
clear
View Solution play_arrow
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question_answer55)
The equation of the circle which touches x-axis at (3, 0) and passes through (1, 4) is given by [MP PET 1993]
A)
\[{{x}^{2}}+{{y}^{2}}-6x-5y+9=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+6x+5y-9=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-6x+5y-9=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+6x-5y+9=0\] done
clear
View Solution play_arrow
-
question_answer56)
If the lines \[x+y=6\] and \[x+2y=4\] be diameters of the circle whose diameter is 20, then the equation of the circle is
A)
\[{{x}^{2}}+{{y}^{2}}-16x+4y-32=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+16x+4y-32=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+16x+4y+32=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+16x-4y+32=0\] done
clear
View Solution play_arrow
-
question_answer57)
The number of circles touching the lines \[x=0\], \[y=a\] and \[y=b\] is
A)
One done
clear
B)
Two done
clear
C)
Four done
clear
D)
Infinite done
clear
View Solution play_arrow
-
question_answer58)
The equation of the circle whose diameters have the end points (a, 0) (0, b) is given by [MP PET 1993]
A)
\[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+ax-by=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-ax+by=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done
clear
View Solution play_arrow
-
question_answer59)
The centre and radius of the circle \[2{{x}^{2}}+2{{y}^{2}}-x=0\] are [MP PET 1984, 87]
A)
\[\left( \frac{1}{4},\ 0 \right)\] and \[\frac{1}{4}\] done
clear
B)
\[\left( -\frac{1}{2},\ 0 \right)\] and \[\frac{1}{2}\] done
clear
C)
\[\left( \frac{1}{2},\ 0 \right)\] and \[\frac{1}{2}\] done
clear
D)
\[\left( 0,\ -\frac{1}{4} \right)\] and \[\frac{1}{4}\] done
clear
View Solution play_arrow
-
question_answer60)
Centre of the circle \[{{(x-3)}^{2}}+{{(y-4)}^{2}}=5\] is [MP PET 1988]
A)
(3, 4) done
clear
B)
\[(-3,\ -4)\] done
clear
C)
(4, 3) done
clear
D)
\[(-4,\ -3)\] done
clear
View Solution play_arrow
-
question_answer61)
The equation of the circle touching \[x=0,y=0\] and \[x=4\] is [UPSEAT 2004]
A)
\[{{x}^{2}}+{{y}^{2}}-4x-4y+16=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-8x-8y+16=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+4x+4y+4=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-4y+4=0\] done
clear
View Solution play_arrow
-
question_answer62)
The equation \[{{x}^{2}}+{{y}^{2}}=0\] denotes [MP PET 1984]
A)
A point done
clear
B)
A circle done
clear
C)
x-axis done
clear
D)
y-axis done
clear
View Solution play_arrow
-
question_answer63)
\[a{{x}^{2}}+2{{y}^{2}}+2bxy+2x-y+c=0\] represents a circle through the origin, if [MP PET 1984]
A)
\[a=0,\ b=0,\ c=2\] done
clear
B)
\[a=1,\ b=0,\ c=0\] done
clear
C)
\[a=2,\ b=2,\ c=0\] done
clear
D)
\[a=2,\ b=0,\ c=0\] done
clear
View Solution play_arrow
-
question_answer64)
Equation of a circle whose centre is origin and radius is equal to the distance between the lines \[x=1\] and \[x=-1\] is [MP PET 1984]
A)
\[{{x}^{2}}+{{y}^{2}}=1\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=\sqrt{2}\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=4\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=-4\] done
clear
View Solution play_arrow
-
question_answer65)
A circle touches the axes at the points (3, 0) and (0, -3). The centre of the circle is [MP PET 1992]
A)
(3, -3) done
clear
B)
(0, 0) done
clear
C)
(-3, 0) done
clear
D)
(6, -6) done
clear
View Solution play_arrow
-
question_answer66)
If the centre of a circle is (2, 3) and a tangent is \[x+y=1\], then the equation of this circle is [RPET 1985, 89]
A)
\[{{(x-2)}^{2}}+{{(y-3)}^{2}}=8\] done
clear
B)
\[{{(x-2)}^{2}}+{{(y-3)}^{2}}=3\] done
clear
C)
\[{{(x+2)}^{2}}+{{(y+3)}^{2}}=2\sqrt{2}\] done
clear
D)
\[{{(x-2)}^{2}}+{{(y-3)}^{2}}=2\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer67)
A circle which passes through origin and cuts intercepts on axes a and b, the equation of circle is [RPET 1991]
A)
\[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-ax+by=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+ax-by=0\] done
clear
View Solution play_arrow
-
question_answer68)
A circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] passing through \[(4,\ -2)\] is concentric to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+20=0\], then the value of c will be [RPET 1984, 86]
A)
? 4 done
clear
B)
4 done
clear
C)
0 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer69)
If the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] represents a circle with x-axis as a diameter and radius a, then
A)
\[f=2a,\ g=0,\ c=3{{a}^{2}}\] done
clear
B)
\[f=0,\ g=a,\ c=3{{a}^{2}}\] done
clear
C)
\[f=0,\ g=-2a,\ c=3{{a}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer70)
The equation of a diameter of circle \[{{x}^{2}}+{{y}^{2}}-6x+2y=0\] passing through origin is [RPET 1991; IIT 1989; MP PET 2002]
A)
\[x+3y=0\] done
clear
B)
\[x-3y=0\] done
clear
C)
\[3x+y=0\] done
clear
D)
\[3x-y=0\] done
clear
View Solution play_arrow
-
question_answer71)
The radius of a circle which touches y-axis at (0,3) and cuts intercept of 8 units with x-axis, is [IIT 1972]
A)
3 done
clear
B)
2 done
clear
C)
5 done
clear
D)
8 done
clear
View Solution play_arrow
-
question_answer72)
A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number\[(\ne 1)\]. Then its locus is [IIT 1982]
A)
Straight line done
clear
B)
Circle done
clear
C)
Parabola done
clear
D)
A pair of straight lines done
clear
View Solution play_arrow
-
question_answer73)
The equation of the circumcircle of the triangle formed by the lines \[y+\sqrt{3}x=6,\ y-\sqrt{3}x=6,\] and \[y=0\], is [EAMCET 1982]
A)
\[{{x}^{2}}+{{y}^{2}}-4y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+4x=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4y=12\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+4x=12\] done
clear
View Solution play_arrow
-
question_answer74)
The equation \[{{x}^{2}}+{{y}^{2}}+4x+6y+13=0\] represents [Roorkee 1990]
A)
Circle done
clear
B)
Pair of coincident straight lines done
clear
C)
Pair of concurrent straight lines done
clear
D)
Point done
clear
View Solution play_arrow
-
question_answer75)
The equation of a circle with centre \[(-4,\ 3)\] and touching the circle \[{{x}^{2}}+{{y}^{2}}=1\], is
A)
\[{{x}^{2}}+{{y}^{2}}+8x-6y+9=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+8x+6y-11=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+8x+6y-9=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer76)
The equation of the circle concentric with the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y-3=0\] and touching y-axis, is
A)
\[{{x}^{2}}+{{y}^{2}}-4x-6y-9=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x-6y+9=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x-6y+3=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer77)
Locus of the centre of the circle touching both the co-ordinates axes is
A)
\[{{x}^{2}}+{{y}^{2}}=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=\]a non-zero constant done
clear
C)
\[{{x}^{2}}-{{y}^{2}}=0\] done
clear
D)
\[{{x}^{2}}-{{y}^{2}}=\]a non-zero constant done
clear
View Solution play_arrow
-
question_answer78)
A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distance of the tangents to the circle at the points A and B respectively from the origin, the diameter of the circle is
A)
\[m(m+n)\] done
clear
B)
\[m+n\] done
clear
C)
\[n(m+n)\] done
clear
D)
\[\frac{1}{2}(m+n)\] done
clear
View Solution play_arrow
-
question_answer79)
Radius of the circle \[{{x}^{2}}+{{y}^{2}}+2x\cos \theta \] \[+2y\sin \theta -8=0\], is [MNR 1974]
A)
1 done
clear
B)
3 done
clear
C)
\[2\sqrt{3}\] done
clear
D)
\[\sqrt{10}\] done
clear
View Solution play_arrow
-
question_answer80)
If the lines \[{{l}_{1}}x+{{m}_{1}}y+{{n}_{1}}=0\] and \[{{l}_{2}}x+{{m}_{2}}y+{{n}_{2}}=0\] cuts the axes at con-cyclic points, then
A)
\[{{l}_{1}}{{l}_{2}}={{m}_{1}}{{m}_{2}}\] done
clear
B)
\[{{l}_{1}}{{m}_{1}}={{l}_{2}}{{m}_{2}}\] done
clear
C)
\[{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}=0\] done
clear
D)
\[{{l}_{1}}{{m}_{2}}={{l}_{2}}{{m}_{1}}\] done
clear
View Solution play_arrow
-
question_answer81)
The locus of a point which moves such that the sum of the squares of its distances from the three vertices of a triangle is constant, is a circle whose centre is at the
A)
Incentre of the triangle done
clear
B)
Centroid of the triangle done
clear
C)
Orthocentre of the triangle done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer82)
Locus of the points from which perpendicular tangent can be drawn to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], is
A)
A circle passing through origin done
clear
B)
A circle of radius 2a done
clear
C)
A concentric circle of radius \[a\sqrt{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer83)
The locus of the centre of a circle which always passes through the fixed points (a, 0) and \[(-a,\ 0)\], is
A)
\[x=1\] done
clear
B)
\[x+y=6\] done
clear
C)
\[x+y=2a\] done
clear
D)
\[x=0\] done
clear
View Solution play_arrow
-
question_answer84)
The equation to a circle whose centre lies at the point (-2, 1) and which touches the line \[3x-2y-6=0\] at (4, 3), is
A)
\[{{x}^{2}}+{{y}^{2}}+4x-2y-35=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x+2y+35=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+4x+2y+35=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer85)
The equation of a circle passing through the point (4, 5) and having the centre at (2, 2) is [UPSEAT 2000]
A)
\[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x=13\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\] done
clear
View Solution play_arrow
-
question_answer86)
The locus of the centre of a circle which touches externally the circle \[{{x}^{2}}+{{y}^{2}}-6x-6y+14=0\] and also touches the y-axis, is given by the equation [IIT 1993; DCE 2000]
A)
\[{{x}^{2}}-6x-10y+14=0\] done
clear
B)
\[{{x}^{2}}-10x-6y+14=0\] done
clear
C)
\[{{y}^{2}}-6x-10y+14=0\] done
clear
D)
\[{{y}^{2}}-10x-6y+14=0\] done
clear
View Solution play_arrow
-
question_answer87)
The area of a circle whose centre is (h, k) and radius a is [MP PET 1994]
A)
\[\pi ({{h}^{2}}+{{k}^{2}}-{{a}^{2}})\] done
clear
B)
\[\pi {{a}^{2}}hk\] done
clear
C)
\[\pi {{a}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer88)
If the equation \[\frac{K{{(x+1)}^{2}}}{3}+\frac{{{(y+2)}^{2}}}{4}=1\] represents a circle, then \[K=\] [MP PET 1994]
A)
3/4 done
clear
B)
1 done
clear
C)
4/3 done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer89)
A circle has radius 3 units and its centre lies on the line \[y=x-1\]. Then the equation of this circle if it passes through point (7,3), is [Roorkee 1988]
A)
\[{{x}^{2}}+{{y}^{2}}-8x-6y+16=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+8x+6y+16=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-8x-6y-16=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer90)
The equation of circle whose diameter is the line joining the points (?4, 3) and (12, ?1) is [IIT 1971; RPET 1984, 87, 89; MP PET 1984; Roorkee 1969; AMU 1979]
A)
\[{{x}^{2}}+{{y}^{2}}+8x+2y+51=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+8x-2y-51=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+8x+2y-51=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-8x-2y-51=0\] done
clear
View Solution play_arrow
-
question_answer91)
The equation of the circle which passes through the points \[(3,\ -2)\] and \[(-2,\ 0)\] and centre lies on the line \[2x-y=3\], is [Roorkee 1971]
A)
\[{{x}^{2}}+{{y}^{2}}-3x-12y+2=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-3x+12y+2=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+3x+12y+2=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer92)
The locus of the centre of a circle of radius 2 which rolls on the outside of circle \[{{x}^{2}}+{{y}^{2}}+3x-6y-9=0\], is
A)
\[{{x}^{2}}+{{y}^{2}}+3x-6y+5=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+3x-6y-31=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+3x-6y+\frac{29}{4}=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer93)
Area of the circle in which a chord of length \[\sqrt{2}\] makes an angle \[\frac{\pi }{2}\] at the centre is
A)
\[\frac{\pi }{2}\] done
clear
B)
\[2\pi \] done
clear
C)
\[\pi \] done
clear
D)
\[\frac{\pi }{4}\] done
clear
View Solution play_arrow
-
question_answer94)
The circle passing through point of intersection of the circle \[S=0\] and the line \[P=0\] is [RPET 1995]
A)
\[S+\lambda P=0\] done
clear
B)
\[S-\lambda P=0\] done
clear
C)
\[\lambda S+P=0\] done
clear
D)
\[P-\lambda S=0\] done
clear
E)
All of these done
clear
View Solution play_arrow
-
question_answer95)
If the coordinates of one end of the diameter of the circle \[{{x}^{2}}+{{y}^{2}}-8x-4y+c=0\] are (-3, 2), then the coordinates of other end are [Roorkee 1995]
A)
(5, 3) done
clear
B)
(6, 2) done
clear
C)
(1, -8) done
clear
D)
(11, 2) done
clear
View Solution play_arrow
-
question_answer96)
For \[a{{x}^{2}}+2hxy+3{{y}^{2}}+4x+8y-6=0\] to represent a circle, one must have
A)
\[a=3,\ h=0\] done
clear
B)
\[a=1,\ h=0\] done
clear
C)
\[a=h=3\] done
clear
D)
\[a=h=0\] done
clear
View Solution play_arrow
-
question_answer97)
A line is drawn through a fixed point \[P(\alpha ,\ \beta )\] to cut the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\] at A and B. Then \[PA\ .\ PB\] is equal to
A)
\[{{(\alpha +\beta )}^{2}}-{{r}^{2}}\] done
clear
B)
\[{{(\alpha +\beta )}^{2}}-{{r}^{2}}\] done
clear
C)
\[{{(\alpha -\beta )}^{2}}+{{r}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer98)
The centre of the circle \[x=-1+2\cos \theta \], \[y=3+2\sin \theta \], is [MP PET 1995]
A)
(1, ?3) done
clear
B)
(?1, 3) done
clear
C)
(1, 3) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer99)
If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at \[(2,\ y)\], then the value of x and y are
A)
\[x=1,\ y=4\] done
clear
B)
\[x=4,\ y=1\] done
clear
C)
\[x=8,\ y=2\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer100)
Circles are drawn through the point (2, 0) to cut intercept of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is
A)
\[{{x}^{2}}+{{y}^{2}}+9x+2fy+14=0\] done
clear
B)
\[3{{x}^{2}}+3{{y}^{2}}+27x-2fy+42=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-9x+2fy+14=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2fy-9y+14=0\] done
clear
View Solution play_arrow
-
question_answer101)
Equations to the circles which touch the lines \[3x-4y+1=0\], \[4x+3y-7=0\]and pass through (2, 3) are [EAMCET 1989]
A)
\[{{(x-2)}^{2}}+{{(y-8)}^{2}}=25\] done
clear
B)
\[5{{x}^{2}}+5{{y}^{2}}-12x-24y+31=0\] done
clear
C)
Both (a) and (b) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer102)
The equation of the circle in the first quadrant which touches each axis at a distance 5 from the origin is [MP PET 1997]
A)
\[{{x}^{2}}+{{y}^{2}}+5x+5y+25=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-10x-10y+25=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-5x-5y+25=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+10x+10y+25=0\] done
clear
View Solution play_arrow
-
question_answer103)
The equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible, is
A)
\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-x-y=0\] done
clear
C)
\[2{{x}^{2}}+2{{y}^{2}}-3x-3y+1=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-3x-3y+2=0\] done
clear
View Solution play_arrow
-
question_answer104)
The equation of the circumcircle of the triangle formed by the lines \[x=0,y=0,2x+3y=5\] is [MP PET 2004]
A)
\[{{x}^{2}}+{{y}^{2}}+2x+3y-5=0\] done
clear
B)
\[6({{x}^{2}}+{{y}^{2}})-5\text{ }(3x+2y)=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x-3y+5=0\] done
clear
D)
\[6({{x}^{2}}+{{y}^{2}})+5\text{ }(3x+2y)=0\] done
clear
View Solution play_arrow
-
question_answer105)
If \[(\alpha ,\beta )\]is the centre of a circle passing through the origin, then its equation is [MP PET 1999]
A)
\[{{x}^{2}}+{{y}^{2}}-\alpha x-\beta y=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+2\alpha x+2\beta y=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2\alpha x-2\beta y=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}+\alpha x+\beta y=0\] done
clear
View Solution play_arrow
-
question_answer106)
The equation \[2{{x}^{2}}+2{{y}^{2}}+4x+8y+15=0\] represents [Roorkee 1999]
A)
A pair of straight lines done
clear
B)
A circle done
clear
C)
An ellipse done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer107)
The equation of the circle whose diameter lies on \[2x+3y=3\]and \[16x-y=4\] which passes through (4,6) is [Kurukshetra CEE 1998]
A)
\[5\text{ }({{x}^{2}}+{{y}^{2}})-3x-8y=200\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x-8y=200\] done
clear
C)
\[5\text{ }({{x}^{2}}+{{y}^{2}})-4x=200\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=40\] done
clear
View Solution play_arrow
-
question_answer108)
The area of the curve \[{{x}^{2}}+{{y}^{2}}=2ax\]is [MP PET 1996]
A)
\[\pi {{a}^{2}}\] done
clear
B)
\[2\pi {{a}^{2}}\] done
clear
C)
\[4\pi {{a}^{2}}\] done
clear
D)
\[\frac{1}{2}\pi {{a}^{2}}\] done
clear
View Solution play_arrow
-
question_answer109)
Radius of the circle \[(x-1)(x-3)+(y-2)(y-4)\] \[=0\] is
A)
2 done
clear
B)
\[\sqrt{2}\] done
clear
C)
3 done
clear
D)
\[2\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer110)
The equation of circle whose centre lies on \[3x-y-4=0\]and\[x+3y+2=0\]and has an area 154 square units is [DCE 2001]
A)
\[{{x}^{2}}+{{y}^{2}}-2x+2y-47=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x+2y+47=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x-2y-47=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer111)
The circle \[{{x}^{2}}+{{y}^{2}}-8x+4y+4=0\]touches [Karnataka CET 1999, 2004; Pb. CET 2000]
A)
x-axis only done
clear
B)
y- axis only done
clear
C)
Both x and y- axis done
clear
D)
Does not touch any axis done
clear
View Solution play_arrow
-
question_answer112)
The equation of circle with centre (1, 2) and tangent \[x+y-5=0\]is [MP PET 2001]
A)
\[{{x}^{2}}+{{y}^{2}}+2x-4y+6=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x+4y+8=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2x-4y+8=0\] done
clear
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question_answer113)
The equation of the circle passing through the point (?2, 4) and through the points of intersection of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y+6=0\] and the line \[3x+2y-5=0\], is [RPET 1996]
A)
\[{{x}^{2}}+{{y}^{2}}+2x-4y-4=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+4x-2y-4=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-3x-4y=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-2y=0\] done
clear
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question_answer114)
The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is [EAMCET 2002]
A)
\[{{(x-5)}^{2}}+{{(y+5)}^{2}}=25\] done
clear
B)
\[{{(x+4)}^{2}}+{{(y+4)}^{2}}=25\] done
clear
C)
\[{{(x+6)}^{2}}+{{(y+6)}^{2}}=25\] done
clear
D)
\[{{(x+5)}^{2}}+{{(y+5)}^{2}}=25\] done
clear
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question_answer115)
The circle \[{{x}^{2}}+{{y}^{2}}-3x-4y+2=0\]cuts x-axis at [Karnataka CET 2001; Pb. CET 2002]
A)
\[(2,\,0),(-3,\,0)\] done
clear
B)
\[(3,\,0),(4,\,0)\] done
clear
C)
\[(1,\,0),(-1,\,0)\] done
clear
D)
\[(1,\,0),(2,\,0)\] done
clear
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question_answer116)
If \[{{g}^{2}}+{{f}^{2}}=c\], then the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]will represent [MP PET 2003]
A)
A circle of radius g done
clear
B)
A circle of radius f done
clear
C)
A circle of diameter \[\sqrt{c}\] done
clear
D)
A circle of radius 0 done
clear
View Solution play_arrow
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question_answer117)
The centre of a circle is (2, ?3) and the circumference is \[10\pi \]. Then the equation of the circle is [Kerala (Engg.) 2002]
A)
\[{{x}^{2}}+{{y}^{2}}+4x+6y+12=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x+6y+12=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x+6y-12=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] done
clear
View Solution play_arrow
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question_answer118)
A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is [EAMCET 2002]
A)
A circle done
clear
B)
An Ellipse done
clear
C)
A hyperbola done
clear
D)
A parabola done
clear
View Solution play_arrow
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question_answer119)
The limit of the perimeter of the regular n-gons inscribed in a circle of radius R as \[n\to \infty \]is [MP PET 2003]
A)
\[2\,\pi \,R\] done
clear
B)
\[\pi \,R\] done
clear
C)
\[4R\] done
clear
D)
\[\pi \,{{R}^{2}}\] done
clear
View Solution play_arrow
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question_answer120)
The centre of circle inscribed in square formed by the lines \[{{x}^{2}}-8x+12=0\]and \[{{y}^{2}}-14y+45=0\], is [IIT Screening 2003]
A)
(4, 7) done
clear
B)
(7, 4) done
clear
C)
(9, 4) done
clear
D)
(4, 9) done
clear
View Solution play_arrow
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question_answer121)
For what value of k, the points (0, 0), (1, 3), (2, 4) and (k, 3) are con-cyclic [RPET 1997]
A)
2 done
clear
B)
1 done
clear
C)
4 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer122)
The four distinct points (0, 0),(2, 0), (0, -2) and (k, -2)are con-cyclic, if k = [EAMCET 2002]
A)
- 2 done
clear
B)
2 done
clear
C)
1 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer123)
Through which of the following pairs of points does the circle \[{{x}^{2}}+{{y}^{2}}-12x+1=0\]pass [MP PET 1983]
A)
(?1, 0), \[(6,\sqrt{35})\] done
clear
B)
\[(3,-\sqrt{26}),(-3,\sqrt{26})\] done
clear
C)
\[(6,-\sqrt{35})\], \[(3,-\sqrt{26})\] done
clear
D)
\[(0,\,-1),(-6,-\sqrt{35})\] done
clear
View Solution play_arrow
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question_answer124)
The radius of the circle passing through the point (6, 2) and two of whose diameters are \[x+y=6\]and \[x+2y=4\]is [Karnataka CET 2004]
A)
4 done
clear
B)
6 done
clear
C)
20 done
clear
D)
\[\sqrt{20}\] done
clear
View Solution play_arrow
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question_answer125)
If the lines \[2x+3y+1=0\]and \[3x-y-4=0\]lie along diameters of a circle of circumference \[10\pi \], then the equation of the circle is [AIEEE 2004]
A)
\[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-23=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2x+2y-23=0\] done
clear
View Solution play_arrow
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question_answer126)
The equation of a circle touching the axes of coordinates and the line \[x\cos \alpha +y\sin \alpha =2\]can be
A)
\[{{x}^{2}}+{{y}^{2}}-2gx-2gy+{{g}^{2}}=0\], where \[g=\frac{2}{(\cos \alpha +\sin \alpha +1)}\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2gx-2gy+{{g}^{2}}=0\], where \[g=\frac{2}{(\cos \alpha +\sin \alpha -1)}\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2gx+2gy+{{g}^{2}}=0\], where \[g=\frac{2}{(\cos \alpha -\sin \alpha +1)}\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2gx+2gy+{{g}^{2}}=0\] where \[g=\frac{2}{(\cos \alpha +\sin \alpha +1)}\] done
clear
E)
All of these done
clear
View Solution play_arrow
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question_answer127)
If a circle and a square have the same perimeter, then [Pb. CET 2001]
A)
Their area are equal done
clear
B)
Area of circle is larger done
clear
C)
Area of square is larger done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer128)
The length of intercept, the circle \[{{x}^{2}}+{{y}^{2}}+10x-6y+9=0\] makes on the x-axis is [Pb. CET 2001]
A)
2 done
clear
B)
4 done
clear
C)
6 done
clear
D)
8 done
clear
View Solution play_arrow
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question_answer129)
The equation to the circle with centre (2, 1) and touching the line \[3x+4y=5\] is [Karnataka CET 2005]
A)
\[{{x}^{2}}+{{y}^{2}}-4x-2y+5=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-4x-2y-5=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-2y-4=0\] done
clear
View Solution play_arrow
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question_answer130)
The centre of the circle \[x=2+3\cos \theta \], \[y=3\sin \theta -1\] is [Karnataka CET 2005]
A)
(3, 3) done
clear
B)
\[(2,\,\,-1)\] done
clear
C)
\[(-2,\,\,1)\] done
clear
D)
\[(-1,\,\,2)\] done
clear
View Solution play_arrow
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question_answer131)
The radius of the circle \[{{x}^{2}}+{{y}^{2}}+4x+6y+13=0\] is [Karnataka CET 2005]
A)
\[\sqrt{26}\] done
clear
B)
\[\sqrt{13}\] done
clear
C)
\[\sqrt{23}\] done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer132)
Let \[P({{x}_{1}},{{y}_{1}})\] and \[Q({{x}_{2}},{{y}_{2}})\]are two points such that their abscissa \[{{x}_{1}}\] and \[{{x}_{2}}\] are the roots of the equation \[{{x}^{2}}+2x-3=0\] while the ordinates \[{{y}_{1}}\] and \[{{y}_{2}}\] are the roots of the equation\[{{y}^{2}}+4y-12=0\]. The centre of the circle with PQ as diameter is [Orissa JEE 2005]
A)
\[(-1,-2)\] done
clear
B)
\[(1,\,\,2)\] done
clear
C)
\[(1,-2)\] done
clear
D)
\[(-1,2)\] done
clear
View Solution play_arrow
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question_answer133)
Four distinct points \[(2k,\,3k),(1,0)(0,1)\]and \[(0,0)\] lie on a circle for [DCE 2005]
A)
\[\,k\in I\] done
clear
B)
\[k<0\] done
clear
C)
\[0<k<1\] done
clear
D)
For two values of k done
clear
View Solution play_arrow
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question_answer134)
If one end of the diameter is (1, 1) and other end lies on the line \[x+y=3\], then locus of centre of circle is [AMU 2005]
A)
\[x+y=1\] done
clear
B)
\[2(x-y)=5\] done
clear
C)
\[2x+2y=5\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer135)
A circle is drawn to cut a chord of length 2a units along X-axis and to touch the Y-axis. The locus of the centre of the circle is [Kerala (Engg.) 2005]
A)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\] done
clear
C)
\[x+y={{a}^{2}}\] done
clear
D)
\[{{x}^{2}}-{{y}^{2}}=4{{a}^{2}}\] done
clear
E)
\[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\] done
clear
View Solution play_arrow