
question_answer1) The new coordinates of a point (4, 5), when the origin is shifted to the point (1,2) are [MNR 1988; IIT 1989; UPSEAT 2000]
A) (5, 3)
B) (3, 5)
C) (3, 7)
D) None of these
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question_answer2) Without changing the direction of coordinate axes, origin is transferred to \[(h,k)\], so that the linear (one degree) terms in the equation \[{{x}^{2}}+{{y}^{2}}4x+6y7\]=0 are eliminated. Then the point \[(h,k)\]is
A) (3, 2)
B) ( 3, 2)
C) (2,  3)
D) None of these
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question_answer3) The equation of the locus of a point whose distance from (a, 0) is equal to its distance from yaxis, is [MP PET 1986]
A) \[{{y}^{2}}2ax={{a}^{2}}\]
B) \[{{y}^{2}}2ax+{{a}^{2}}=0\]
C) \[{{y}^{2}}+2ax+{{a}^{2}}=0\]
D) \[{{y}^{2}}+2ax={{a}^{2}}\]
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question_answer4) Two points A and B have coordinates (1, 0) and (1, 0) respectively and Q is a point which satisfies the relation \[AQBQ=\]\[\pm 1.\]The locus of Q is [MP PET 1986]
A) \[12{{x}^{2}}+4{{y}^{2}}=3\]
B) \[12{{x}^{2}}4{{y}^{2}}=3\]
C) \[12{{x}^{2}}4{{y}^{2}}+3=0\]
D) \[12{{x}^{2}}+4{{y}^{2}}+3=0\]
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question_answer5) The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope \[\sqrt{3}\] is
A) \[x\sqrt{3}y=0\]
B) \[x+\sqrt{3}y=0\]
C) \[\sqrt{3}x+y=0\]
D) \[\sqrt{3}xy=0\]
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question_answer6) If the coordinates of a point be given by the equation \[x=a(1\cos \theta ),\]\[y=a\sin \theta \], then the locus of the point will be
A) A straight line
B) A circle
C) A parabola
D) An ellipse
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question_answer7) If P = (1,0), Q =(1,0) and R =(2,0) are three given points, then the locus of a point S satisfying the relation \[S{{Q}^{2}}+S{{R}^{2}}=2S{{P}^{2}}\] is [IIT 1988]
A) A straight line parallel to xaxis
B) A circle through origin
C) A circle with centre at the origin
D) A straight line parallel to yaxis
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question_answer8) The coordinates of the points O, A and B are (0,0), (0,4) and (6,0) respectively. If a points P moves such that the area of \[\Delta POA\]is always twice the area of \[\Delta POB\], then the equation to both parts of the locus of P is [IIT 1964]
A) \[(x3y)(x+3y)=0\]
B) \[(x3y)(x+y)=0\]
C) \[(3xy)(3x+y)=0\]
D) None of these
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question_answer9) A point moves in such a way that the sum of square of its distance from the points \[A(2,0)\]and\[B(2,0)\]is always equal to the square of the distance between A and B. The locus of the point is
A) \[{{x}^{2}}+{{y}^{2}}2=0\]
B) \[{{x}^{2}}+{{y}^{2}}+2=0\]
C) \[{{x}^{2}}+{{y}^{2}}+4=0\]
D) \[{{x}^{2}}+{{y}^{2}}4=0\]
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question_answer10) A point P moves so that its distance from the point \[(a,0)\]is always equal to its distance from the line \[x+a=0\]. The locus of the point is [MP PET 1982]
A) \[{{y}^{2}}=4ax\]
B) \[{{x}^{2}}=4ay\]
C) \[{{y}^{2}}+4ax=0\]
D) \[{{x}^{2}}+4ay=0\]
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question_answer11) The equation to the locus of a point which moves so that its distance from xaxis is always one half its distance from the origin, is
A) \[{{x}^{2}}+3{{y}^{2}}=0\]
B) \[{{x}^{2}}3{{y}^{2}}=0\]
C) \[3{{x}^{2}}+{{y}^{2}}=0\]
D) \[3{{x}^{2}}{{y}^{2}}=0\]
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question_answer12) A point moves so that its distance from the point (1, 0) is always three times its distance from the point (0, 2). The locus of the point is
A) A line
B) A circle
C) A parabola
D) An ellipse
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question_answer13) The locus of a point which moves so that its distance from xaxis is double of its distance from yaxis is [AMU 1978; MP PET 1984]
A) \[x=2y\]
B) \[y=2x\]
C) \[x=5y+1\]
D) \[y=2x+3\]
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question_answer14) O is the origin and A is the point (3, 4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is
A) \[4x3y=0\]
B) \[4x+3y=0\]
C) \[3x+4y=0\]
D) \[3x4y=0\]
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question_answer15) The locus of a point which moves so that it is always equidistant from the point A(a, 0) and B ( a, 0) is [MP PET 1984]
A) A circle
B) Perpendicular bisector of the line segment AB
C) A line parallel to xaxis
D) None of these
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question_answer16) The coordinates of the points A and B are (a, 0) and \[(a,\,0)\] respectively. If a point P moves so that \[P{{A}^{2}}P{{B}^{2}}=2{{k}^{2}}\], when k is constant, then the equation to the locus of the point P , is
A) \[2ax{{k}^{2}}=0\]
B) \[2ax+{{k}^{2}}=0\]
C) \[2ay{{k}^{2}}=0\]
D) \[2ay+{{k}^{2}}=0\]
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question_answer17) If the coordinates of a point be given by the equations \[x=b\sec \varphi ,\ \ y=a\tan \varphi \], then its locus is
A) A straight line
B) A circle
C) An ellipse
D) A hyperbola
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question_answer18) The coordinates of the point A and B are \[(ak,0)\] and\[\left( \frac{a}{k},0 \right),\,\,(k=\pm 1)\]. If a point P moves so that \[PA=kPB,\] then the equation to the locus of P is
A) \[{{k}^{2}}({{x}^{2}}+{{y}^{2}}){{a}^{2}}=0\]
B) \[{{x}^{2}}+{{y}^{2}}{{k}^{2}}{{a}^{2}}=0\]
C) \[{{x}^{2}}+{{y}^{2}}+{{a}^{2}}=0\]
D) \[{{x}^{2}}+{{y}^{2}}{{a}^{2}}=0\]
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question_answer19) The locus of a point which moves in such a way that its distance from (0,0) is three times its distance from the xaxis, as given by [MP PET 1993]
A) \[{{x}^{2}}8{{y}^{2}}=0\]
B) \[{{x}^{2}}+8{{y}^{2}}=0\]
C) \[4{{x}^{2}}{{y}^{2}}=0\]
D) \[{{x}^{2}}4{{y}^{2}}=0\]
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question_answer20) The equation of the locus of all points equidistant from the point (4,2) and the xaxis, is [CEE 1993]
A) \[{{x}^{2}}+8x+4y20=0\]
B) \[{{x}^{2}}8x4y+20=0\]
C) \[{{y}^{2}}4y8x+20=0\]
D) None of these
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question_answer21) The locus of the midpoint of the distance between the axes of the variable line \[x\cos \alpha +y\sin \alpha =p,\]where p is constant, is [MNR 1985; CEE 1993; UPSEAT 2000; AIEEE 2002]
A) \[{{x}^{2}}+{{y}^{2}}=4{{p}^{2}}\]
B) \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{4}{{{p}^{2}}}\]
C) \[{{x}^{2}}+{{y}^{2}}=\frac{4}{{{p}^{2}}}\]
D) \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{2}{{{p}^{2}}}\]
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question_answer22) The locus of a point whose distance from the point \[(g,f)\]is always 'a', will be, (where \[k={{g}^{2}}+{{f}^{2}}{{a}^{2}}\])
A) \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+k=0\]
B) \[{{x}^{2}}{{y}^{2}}+2gx+2fy+k=0\]
C) \[{{x}^{2}}+{{y}^{2}}+2xy+2gx+2fy+k=0\]
D) None of these
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question_answer23) The locus of the moving point P, such that 2PA = 3PB where A is (0,0) and B is (4,3), is [AMU 1980]
A) \[5{{x}^{2}}5{{y}^{2}}72x+54y+225=0\]
B) \[5{{x}^{2}}5{{y}^{2}}+72x+54y+225=0\]
C) \[5{{x}^{2}}+5{{y}^{2}}+72x+54y+225=0\]
D) \[5{{x}^{2}}+5{{y}^{2}}72x+54y+225=0\]
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question_answer24) A point moves such that the sum of its distances from two fixed points (ae,0) and (ae,0) is always 2a. Then equation of its locus is [MNR 1981]
A) \[\]\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1{{e}^{2}})}=1\]
B) \[\frac{{{x}^{2}}}{{{a}^{2}}}\frac{{{y}^{2}}}{{{a}^{2}}(1{{e}^{2}})}=1\]
C) \[\frac{{{x}^{2}}}{{{a}^{2}}(1{{e}^{2}})}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\]
D) None of these
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question_answer25) A point moves in such a way that its distance from (1,2) is always the twice from (3,5), the locus of the point is
A) \[3{{x}^{2}}+{{y}^{2}}+26x+44y131=0\]
B) \[{{x}^{2}}+3{{y}^{2}}26x+44y131=0\]
C) \[3({{x}^{2}}+{{y}^{2}})+26x44y+131=0\]
D) None of these
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question_answer26) A point moves in such a way that its distance from origin is always 4. Then the locus of the point is
A) \[{{x}^{2}}+{{y}^{2}}=4\]
B) \[{{x}^{2}}+{{y}^{2}}=16\]
C) \[{{x}^{2}}+{{y}^{2}}=2\]
D) None of these
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question_answer27) If \[A(a,0)\] and \[B(a,0)\]are two fixed points, then the locus of the point on which the line AB subtends the right angle, is
A) \[{{x}^{2}}+{{y}^{2}}=2{{a}^{2}}\]
B) \[{{x}^{2}}{{y}^{2}}={{a}^{2}}\]
C) \[{{x}^{2}}+{{y}^{2}}+{{a}^{2}}=0\]
D) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
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question_answer28) If A and B are two fixed points and P is a variable point such that \[PA+PB=4\], then the locus of P is a/an [IIT 1989; MNR 1991; UPSEAT 2000]
A) Parabola
B) Ellipse
C) Hyperbola
D) None of these
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question_answer29) If A and B are two points in a plane, so that \[PAPB\] = constant, then the locus of P is [MNR 1991, 95]
A) Hyperbola
B) Circle
C) Parabola
D) Ellipse
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question_answer30) If A and B are two fixed points in a plane and P is another variable point such that \[P{{A}^{2}}+P{{B}^{2}}=\]constant, then the locus of the point P is [MNR 1991]
A) Hyperbola
B) Circle
C) Parabola
D) Ellipse
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question_answer31) The locus of P such that area of \[\Delta PAB=12sq.\] units, where \[A(2,3)\] and \[B(4,5)\] is [EAMCET 1989]
A) \[(x+3y1)(x+3y23)=0\]
B) \[(x+3y+1)(x+3y23)=0\]
C) \[(3x+y1)(3x+y23)=0\]
D) \[(3x+y+1)(3x+y+23)=0\]
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question_answer32) The position of a moving point in the XYplane at time t is given by \[\left( (u\cos \alpha )t,(u\sin \alpha )t\frac{1}{2}g{{t}^{2}} \right),\] where \[u,\,\alpha ,\,g\]are constants. The locus of the moving point is
A) A circle
B) A parabola
C) An ellipse
D) None of these
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question_answer33) If \[A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,\cos \alpha ),\,C(1,\text{ }2)\]are the vertices of a \[\Delta ABC\], then as \[\alpha \]varies, the locus of its centroid is
A) \[{{x}^{2}}+{{y}^{2}}2x4y+1=0\]
B) \[3({{x}^{2}}+{{y}^{2}})2x4y+1=0\]
C) \[{{x}^{2}}+{{y}^{2}}2x4y+3=0\]
D) None of these
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question_answer34) If the equation of the locus of a point equidistant from the points \[({{a}_{1}},{{b}_{1}})\] and \[({{a}_{2}},{{b}_{2}})\] is \[({{a}_{1}}{{a}_{2}})x+({{b}_{1}}{{b}_{2}})y+c=0\], then the value of c is
A) \[a_{1}^{2}a_{2}^{2}+b_{1}^{2}b_{2}^{2}\]
B) \[\sqrt{a_{1}^{2}+b_{1}^{2}a_{2}^{2}b_{2}^{2}}\]
C) \[\frac{1}{2}(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2})\]
D) \[\frac{1}{2}(a_{2}^{2}+b_{2}^{2}a_{1}^{2}b_{1}^{2})\]
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question_answer35) If sum of distances of a point from the origin and lines \[x=2\] is 4, then its locus is [RPET 1997]
A) \[{{x}^{2}}12y=36\]
B) \[{{y}^{2}}+12x=36\]
C) \[{{y}^{2}}12x=36\]
D) \[{{x}^{2}}+12y=36\]
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question_answer36) The locus of a point whose difference of distance from points (3, 0) and (3,0) is 4, is [MP PET 2002]
A) \[\frac{{{x}^{2}}}{4}\frac{{{y}^{2}}}{5}=1\]
B) \[\frac{{{x}^{2}}}{5}\frac{{{y}^{2}}}{4}=1\]
C) \[\frac{{{x}^{2}}}{2}\frac{{{y}^{2}}}{3}=1\]
D) \[\frac{{{x}^{2}}}{3}\frac{{{y}^{2}}}{2}=1\]
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question_answer37) Locus of centroid of the triangle whose vertices are \[(a\cos t,a\sin t),\ (b\sin t,b\cos t)\] and (1, 0), where t is a parameter; is [AIEEE 2003]
A) \[{{(3x1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}{{b}^{2}}\]
B) \[{{(3x1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
C) \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
D) \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}{{b}^{2}}\]
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question_answer38) If the distance of any point P from the point \[A(a+b,ab)\] and \[B(ab,a+b)\]are equal, then the locus of P is [Karnataka CET 2003]
A) \[xy=0\]
B) \[ax+by=0\]
C) \[bxay=0\]
D) \[x+y=0\]
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question_answer39) What is the equation of the locus of a point which moves such that 4 times its distance from the xaxis is the square of its distance from the origin [Karnataka CET 2004]
A) \[{{x}^{2}}+{{y}^{2}}4y=0\]
B) \[{{x}^{2}}+{{y}^{2}}4y=0\]
C) \[{{x}^{2}}+{{y}^{2}}4x=0\]
D) \[{{x}^{2}}+{{y}^{2}}4x=0\]
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question_answer40) Let P be the point (1, 0) and Q a point of the locus\[{{y}^{2}}=8x\]. The locus of midpoint of PQ is [AIEEE 2005]
A) \[{{x}^{2}}+4y+2=0\]
B) \[{{x}^{2}}4y+2=0\]
C) \[{{y}^{2}}4x+2=0\]
D) \[{{y}^{2}}+4x+2=0\]
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