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question_answer1)
The coordinates of the foot of the perpendicular from the point (2, 3) on the line \[y=3x+4\] are given by [MP PET 1984]
A)
\[\left( \frac{37}{10},-\frac{1}{10} \right)\] done
clear
B)
\[\left( -\frac{1}{10},\frac{37}{10} \right)\] done
clear
C)
\[\left( \frac{10}{37},-10 \right)\] done
clear
D)
\[\left( \frac{2}{3},-\frac{1}{3} \right)\] done
clear
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question_answer2)
Coordinates of the foot of the perpendicular drawn from (0,0) to the line joining \[(a\cos \alpha ,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\] are [IIT 1982]
A)
\[\left( \frac{a}{2},\frac{b}{2} \right)\] done
clear
B)
\[\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]\] done
clear
C)
\[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\] done
clear
D)
None of these done
clear
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question_answer3)
The coordinates of the foot of the perpendicular from \[({{x}_{1}},{{y}_{1}})\]to the line \[ax+by+c=0\] are [Dhanbad Engg. 1973]
A)
\[\left( \frac{{{b}^{2}}{{x}_{1}}-ab{{y}_{1}}-ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}-ab{{x}_{1}}-bc}{{{a}^{2}}+{{b}^{2}}} \right)\] done
clear
B)
\[\left( \frac{{{b}^{2}}{{x}_{1}}+ab{{y}_{1}}+ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}+ab{{x}_{1}}+bc}{{{a}^{2}}+{{b}^{2}}} \right)\] done
clear
C)
\[\left( \frac{a{{x}_{1}}+b{{y}_{1}}+ab}{a+b},\frac{a{{x}_{1}}-b{{y}_{1}}-ab}{a+b} \right)\] done
clear
D)
None of these done
clear
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question_answer4)
The foot of the coordinates drawn from (2, 4) to the line \[x+y=1\] is [Roorkee 1995]
A)
\[\left( \frac{1}{3},\frac{3}{2} \right)\] done
clear
B)
\[\left( -\frac{1}{2},\frac{3}{2} \right)\] done
clear
C)
\[\left( \frac{4}{3},\frac{1}{2} \right)\] done
clear
D)
\[\left( \frac{3}{4},\,\,-\frac{1}{2} \right)\] done
clear
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question_answer5)
The co-ordinates of the foot of perpendicular from the point (2, 3) on the line \[x+y-11=0\]are [MP PET 1986]
A)
\[(-6,\,5)\] done
clear
B)
\[(5,\,6)\] done
clear
C)
\[(-5,\,6)\] done
clear
D)
\[(6,\,5)\] done
clear
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question_answer6)
The line \[2x+3y=12\]meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to \[AB\]meets the x- axis , y axis and the \[AB\] at C, D and E respectively. If O is the origin of coordinates, then the area of \[OCEB\]is [IIT 1976]
A)
\[23\] sq. units done
clear
B)
\[\frac{23}{2}sq.\]units done
clear
C)
\[\frac{23}{3}sq.\]units done
clear
D)
None of these done
clear
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question_answer7)
If A and B are two points on the line \[3x+4y+15=0\]such that \[OA=OB=9\]units, then the area of the triangle \[OAB\] is
A)
18 sq. units done
clear
B)
\[18\sqrt{2}sq.\]units done
clear
C)
18/\[\sqrt{2}\]sq. units done
clear
D)
None of these done
clear
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question_answer8)
One vertex of the equilateral triangle with centroid at the origin and one side as \[x+y-2=0\]is
A)
\[(-1,-1)\] done
clear
B)
\[(2,2)\] done
clear
C)
\[(-2,-2)\] done
clear
D)
None of these done
clear
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question_answer9)
The point (4, 1)undergoes the following two successive transformation (i) Reflection about the line \[y=x\] (ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are [MNR 1987; UPSEAT 2000]
A)
(4, 3) done
clear
B)
(3, 4) done
clear
C)
(1, 4) done
clear
D)
\[\left( \frac{7}{2},\frac{7}{2} \right)\] done
clear
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question_answer10)
Line L has intercepts a and b on the co-ordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q, then [IIT 1990; Kurukshetra CEE 1998]
A)
\[{{a}^{2}}+{{b}^{2}}={{p}^{2}}+{{q}^{2}}\] done
clear
B)
\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}+\frac{1}{{{q}^{2}}}\] done
clear
C)
\[{{a}^{2}}+{{p}^{2}}={{b}^{2}}+{{q}^{2}}\] done
clear
D)
\[\frac{1}{{{a}^{2}}}+\frac{1}{{{p}^{2}}}=\frac{1}{{{b}^{2}}}+\frac{1}{{{q}^{2}}}\] done
clear
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question_answer11)
Let L be the line \[2x+y=2\]. If the axes are rotated by \[{{45}^{o}}\], then the intercepts made by the line L on the new axes are respectively [Roorkee Qualifying 1998]
A)
\[\sqrt{2}\]and 1 done
clear
B)
1 and \[\sqrt{2}\] done
clear
C)
\[2\sqrt{2}\]and \[2\sqrt{2}/3\] done
clear
D)
\[2\sqrt{2}/3\]and \[2\sqrt{2}\] done
clear
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question_answer12)
The pedal points of a perpendicular drawn from origin on the line \[3x+4y-5=0\], is [RPET 1990]
A)
\[\left( \frac{3}{5},2 \right)\] done
clear
B)
\[\left( \frac{3}{5},\frac{4}{5} \right)\] done
clear
C)
\[\left( -\frac{3}{5},-\frac{4}{5} \right)\] done
clear
D)
\[\left( \frac{30}{17},\frac{19}{17} \right)\] done
clear
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question_answer13)
The image of a point \[A(3,\,8)\]in the line \[x+3y-7=0\], is [RPET 1991]
A)
\[(-1,-4)\] done
clear
B)
\[(-3\,,\,\,-8)\] done
clear
C)
\[(1,-4)\] done
clear
D)
\[(3,\,8)\] done
clear
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question_answer14)
The reflection of the point (4, -13) in the line \[5x+y+6=0\] is [EAMCET 1994]
A)
\[(-1,-14)\] done
clear
B)
(3 ,4) done
clear
C)
(1, 2) done
clear
D)
(- 4, 13) done
clear
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question_answer15)
If (- 2, 6) is the image of the point (4, 2) with respect to line L = 0, then L = [EAMCET 2002]
A)
3x ? 2y + 5 done
clear
B)
3x ? 2y + 10 done
clear
C)
2x + 3y ? 5 done
clear
D)
6x ? 4y ? 7 done
clear
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question_answer16)
A straight line passes through a fixed point \[(h,k)\]. The locus of the foot of perpendicular on it drawn from the origin is
A)
\[{{x}^{2}}+{{y}^{2}}-hx-ky=0\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+hx+ky=0\] done
clear
C)
\[3{{x}^{2}}+3{{y}^{2}}+hx-ky=0\] done
clear
D)
None of these done
clear
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question_answer17)
If for a variable line \[\frac{x}{a}+\frac{y}{b}=1\], the condition \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\] (c is a constant) is satisfied, then locus of foot of perpendicular drawn from origin to the line is [RPET 1999]
A)
\[{{x}^{2}}+{{y}^{2}}={{c}^{2}}/2\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=2{{c}^{2}}\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}={{c}^{2}}\] done
clear
D)
\[{{x}^{2}}-{{y}^{2}}={{c}^{2}}\] done
clear
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