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question_answer1)
The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b), is
A)
\[{{x}^{2}}+{{y}^{2}}-ax-by=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+ax+by=0\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2ax-2by=0\] done
clear
D)
None of these done
clear
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question_answer2)
The orthocentre of the triangle formed by the lines \[xy=0\]and \[x+y=1\]is [IIT 1995]
A)
\[(0,0)\] done
clear
B)
\[\left( \frac{1}{2},\frac{1}{2} \right)\] done
clear
C)
\[\left( \frac{1}{3},\frac{1}{3} \right)\] done
clear
D)
\[\left( \frac{1}{4},\frac{1}{4} \right)\] done
clear
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question_answer3)
The product of perpendiculars drawn from the origin to the lines represented by the equation\[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\], will be [Bihar CEE 1994]
A)
\[\frac{ab}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}\] done
clear
B)
\[\frac{bc}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}\] done
clear
C)
\[\frac{ca}{\sqrt{({{a}^{2}}+{{b}^{2}})+4{{h}^{2}}}}\] done
clear
D)
\[\frac{c}{\sqrt{{{(a-b)}^{2}}+4{{h}^{2}}}}\] done
clear
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question_answer4)
The equations to a pair of opposite sides of a parallelogram are \[{{x}^{2}}-5x+6=0\]and \[{{y}^{2}}-6y+5=0\]. The equations to its diagonals are [IIT 1994; Pb. CET 2003]
A)
\[x+4y=13\]and \[y=4x-7\] done
clear
B)
\[4x+y=13\]and \[4y=x-7\] done
clear
C)
\[4x+y=13\]and \[y=4x-7\] done
clear
D)
\[y-4x=13\]and \[y+4x=7\] done
clear
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question_answer5)
Area of the triangle formed by the lines \[{{y}^{2}}-9xy+18{{x}^{2}}=0\] and \[y=9\] is
A)
\[\frac{27}{4}sq\]. units done
clear
B)
\[27sq.\]units done
clear
C)
\[\frac{27}{2}sq.\] units done
clear
D)
None of these done
clear
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question_answer6)
If the pair of straight lines given by \[A{{x}^{2}}+2Hxy+B{{y}^{2}}=0\], \[({{H}^{2}}>AB)\] forms an equilateral triangle with line \[ax+by+c=0\], then \[(A+3B)(3A+B)\] is [EAMCET 2003]
A)
\[{{H}^{2}}\] done
clear
B)
\[-{{H}^{2}}\] done
clear
C)
\[2{{H}^{2}}\] done
clear
D)
\[4{{H}^{2}}\] done
clear
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question_answer7)
The area (in square units) of the quadrilateral formed by the two pairs of lines\[{{l}^{2}}{{x}^{2}}-{{m}^{2}}{{y}^{2}}-n(lx+my)=0\]and \[{{l}^{2}}{{x}^{2}}-{{m}^{2}}{{y}^{2}}+n(lx-my)=0\] is [EAMCET 2003]
A)
\[\frac{{{n}^{2}}}{2|lm|}\] done
clear
B)
\[\frac{{{n}^{2}}}{|lm|}\] done
clear
C)
\[\frac{n}{2|lm|}\] done
clear
D)
\[\frac{{{n}^{2}}}{4|lm|}\] done
clear
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question_answer8)
The locus of the point \[P(x,y)\] satisfying the relation \[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}+\sqrt{{{(x+3)}^{2}}+{{(y-1)}^{2}}}=6\] is [Orissa JEE 2002]
A)
Straight line done
clear
B)
Pair of straight lines done
clear
C)
Circle done
clear
D)
Ellipse done
clear
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question_answer9)
The square of distance between the point of intersection of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] and origin, is
A)
\[\frac{c(a+b)-{{f}^{2}}-{{g}^{2}}}{ab-{{h}^{2}}}\] done
clear
B)
\[\frac{c(a-b)+{{f}^{2}}+{{g}^{2}}}{\sqrt{ab-{{h}^{2}}}}\] done
clear
C)
\[\frac{c(a+b)-{{f}^{2}}-{{g}^{2}}}{ab+{{h}^{2}}}\] done
clear
D)
None of these done
clear
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question_answer10)
The equation of the pair of straight lines, each of which makes an angle \[\alpha \]with the line \[y=x\], is [MP PET 1990]
A)
\[{{x}^{2}}+2xy\sec 2\alpha +{{y}^{2}}=0\] done
clear
B)
\[{{x}^{2}}+2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] done
clear
C)
\[{{x}^{2}}-2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] done
clear
D)
\[{{x}^{2}}-2xy\sec 2\alpha +{{y}^{2}}=0\] done
clear
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question_answer11)
If the bisectors of the lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\] be \[{{x}^{2}}-2qxy-{{y}^{2}}=0,\] then [MP PET 1993; DCE 1999; RPET 2003; AIEEE 2003; Kerala (Engg.) 2005]
A)
\[pq+1=0\] done
clear
B)
\[pq-1=0\] done
clear
C)
\[p+q=0\] done
clear
D)
\[p-q=0\] done
clear
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question_answer12)
The angle between the pair of straight lines \[{{y}^{2}}{{\sin }^{2}}\theta -xy{{\sin }^{2}}\theta +{{x}^{2}}({{\cos }^{2}}\theta -1)=1,\]is [MNR 1985; UPSEAT 2000; Kerala (Engg.) 2005]
A)
\[\frac{\pi }{3}\] done
clear
B)
\[\frac{\pi }{4}\] done
clear
C)
\[\frac{2\pi }{3}\] done
clear
D)
None of these done
clear
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question_answer13)
The pair of lines represented by \[3a{{x}^{2}}+5xy+({{a}^{2}}-2){{y}^{2}}=0\] are perpendicular to each other for [AIEEE 2002]
A)
Two values of \[a\] done
clear
B)
\[\forall a\] done
clear
C)
For one value of \[a\] done
clear
D)
For no value of \[a\] done
clear
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question_answer14)
The figure formed by the lines \[{{x}^{2}}+4xy+{{y}^{2}}=0\] and \[x-y=4,\] is [Roorkee 1980]
A)
A right angled triangle done
clear
B)
An isosceles triangle done
clear
C)
An equilateral triangle done
clear
D)
None of these done
clear
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question_answer15)
The equation \[{{x}^{2}}-3xy+\lambda {{y}^{2}}+3x-5y+2=0\] when \[\lambda \]is a real number, represents a pair of straight lines. If \[\theta \] is the angle between the lines, then \[\text{cose}{{\text{c}}^{2}}\theta \]= [EAMCET 1992]
A)
3 done
clear
B)
9 done
clear
C)
10 done
clear
D)
100 done
clear
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question_answer16)
If one of the lines of the pair \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] bisects the angle between positive directions of the axes, then a, b, h satisfy the relation [Roorkee 1992]
A)
\[a+b=2|h|\] done
clear
B)
\[a+b=-2h\] done
clear
C)
\[a-b=2|h|\] done
clear
D)
\[{{(a-b)}^{2}}=4{{h}^{2}}\] done
clear
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question_answer17)
The lines joining the origin to the points of intersection of the line \[y=mx+c\]and the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]will be mutually perpendicular, if [Roorkee 1977]
A)
\[{{a}^{2}}({{m}^{2}}+1)={{c}^{2}}\] done
clear
B)
\[{{a}^{2}}({{m}^{2}}-1)={{c}^{2}}\] done
clear
C)
\[{{a}^{2}}({{m}^{2}}+1)={{c}^{2}}\] done
clear
D)
\[{{a}^{2}}({{m}^{2}}-1)=2{{c}^{2}}\] done
clear
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question_answer18)
The angle between the lines joining the points of intersection of line \[y=3x+2\] and the curve \[{{x}^{2}}+2xy+3{{y}^{2}}+4x+8y-11=0\] to the origin, is
A)
\[{{\tan }^{-1}}\left( \frac{3}{2\sqrt{2}} \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( \frac{2}{2\sqrt{2}} \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( \sqrt{3} \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( \frac{2}{2\sqrt{2}} \right)\] done
clear
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question_answer19)
If the lines \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] represents the adjacent sides of a parallelogram, then the equation of second diagonal if one is \[lx+my=1\], will be
A)
\[(am+hl)x=(bl+hm)y\] done
clear
B)
\[(am-hl)x=(bl-hm)y\] done
clear
C)
\[(am-hl)x=(bl+hm)y\] done
clear
D)
None of these done
clear
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question_answer20)
If the pair of lines \[a{{x}^{2}}+2(a+b)xy+b{{y}^{2}}=0\] lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then [AIEEE 2005]
A)
\[3{{a}^{2}}+10ab+3{{b}^{2}}=0\] done
clear
B)
\[3{{a}^{2}}+2ab+3{{b}^{2}}=0\] done
clear
C)
\[3{{a}^{2}}-10ab+3{{b}^{2}}=0\] done
clear
D)
\[3{{a}^{2}}-2ab+3{{b}^{2}}=0\] done
clear
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question_answer21)
The equation of the pair of straight lines parallel to x-axis and touching the circle \[{{x}^{2}}+{{y}^{2}}-6x-4y-12=0\] [Kerala (Engg.) 2002]
A)
\[{{y}^{2}}-4y-21=0\] done
clear
B)
\[{{y}^{2}}+4y-21=0\] done
clear
C)
\[{{y}^{2}}-4y+21=0\] done
clear
D)
\[{{y}^{2}}+4y+21=0\] done
clear
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question_answer22)
Two of the lines represented by the equation \[a{{y}^{4}}+bx{{y}^{3}}+c{{x}^{2}}{{y}^{2}}+d{{x}^{3}}y+e{{x}^{4}}=0\] will be perpendicular, then [Kurukshetra CEE 1998]
A)
\[(b+d)(ad+be)+{{(e-a)}^{2}}(a+c+e)=0\] done
clear
B)
\[(b+d)(ad+be)+{{(e+a)}^{2}}(a+c+e)=0\] done
clear
C)
\[(b-d)(ad-be)+{{(e-a)}^{2}}(a+c+e)=0\] done
clear
D)
\[(b-d)(ad-be)+{{(e+a)}^{2}}(a+c+e)=0\] done
clear
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question_answer23)
The lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] will be equidistant from the origin, if
A)
\[{{f}^{2}}+{{g}^{2}}=c(b-a)\] done
clear
B)
\[{{f}^{4}}+{{g}^{4}}=c(b{{f}^{2}}+a{{g}^{2}})\] done
clear
C)
\[{{f}^{4}}-{{g}^{4}}=c(b{{f}^{2}}-a{{g}^{2}})\] done
clear
D)
\[{{f}^{2}}+{{g}^{2}}=a{{f}^{2}}+b{{g}^{2}}\] done
clear
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question_answer24)
The circumcentre of the triangle formed by the lines \[xy+2x+2y+4=0\] and \[x+y+2=0\] [EAMCET 1994]
A)
(0, 0) done
clear
B)
(-2, - 2) done
clear
C)
(-1, -1) done
clear
D)
(-1, -2) done
clear
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question_answer25)
The area bounded by the angle bisectors of the lines \[{{x}^{2}}-{{y}^{2}}+2y=1\] and the line \[x+y=3\], is [IIT Screening 2004]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
6 done
clear
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