Total Questions:50 Total Time: 75 Min
Remaining:
Question:If a point \((x,\;y) \equiv (\tan \theta + \sin \theta ,\;\tan \theta - \sin \theta )\), then locus of (x, y) is
\({({x^2}y)^{2/3}} + {(x{y^2})^{2/3}} = 1\)
\({x^2} - {y^2} = 4xy\)
\({({x^2} - {y^2})^2} = 16xy\)
\({x^2} - {y^2} = 6xy\)
Question:Equation\(\sqrt {{{(x - 2)}^2} + {y^2}} + \sqrt {{{(x + 2)}^2} + {y^2}} = 4\)represents
Parabola
Ellipse
Circle
Pair of straight lines
Question:If the parabola \({y^2} = 4ax\) passes through (-3, 2), then length of its latus rectum is
2/3
1/3
4/3
4
Question:The ends of latus rectum of parabola \({x^2} + 8y = 0\) are
(–4, –2) and (4, 2)
(4, –2) and (–4, 2)
(–4, –2) and (4, –2)
(4, 2) and (–4, 2)
Question:The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is
\({x^2} + 2x - 2y - 3 = 0\)
\(2{x^2} = 3y\)
\({x^2} - 2x - y + 3 = 0\)
None of these
Question:Axis of the parabola \({x^2} - 4x - 3y + 10 = 0\) is
\(y + 2 = 0\)
\(x + 2 = 0\)
\(y - 2 = 0\)
\(x - 2 = 0\)
Question:If the vertex of the parabola \(y = {x^2} - 8x + c\) lies on x-axis, then the value of c is
16
Question:The points of intersection of the curves whose parametric equations are \(x = {t^2} + 1,\;y = 2t\) and \(x = 2s,\;y = \frac{2}{s}\) is given by
\((1,\; - 3)\)
(2, 2)
(–2, 4)
(1, 2)
Question:The vertex of parabola \({(y - 2)^2} = 16(x - 1)\) is
(2, 1)
(1, –2)
(–1, 2)
Question:Equation of the parabola with its vertex at (1, 1) and focus (3, 1) is
\({(x - 1)^2} = 8(y - 1)\)
\({(y - 1)^2} = 8(x - 3)\)
\({(y - 1)^2} = 8(x - 1)\)
\({(x - 3)^2} = 8(y - 1)\)
Question:The line \(x\cos \alpha + y\sin \alpha = p\) will touch the parabola \({y^2} = 4a(x + a)\), if
\(p\cos \alpha + a = 0\)
\(p\cos \alpha - a = 0\)
\(a\cos \alpha + p = 0\)
\(a\cos \alpha - p = 0\)
Question:The equation of a tangent to the parabola \({y^2} = 4ax\) making an angle \(\theta \) with x-axis is
\(y = x\cot \theta + a\tan \theta \)
\(x = y\tan \theta + a\cot \theta \)
\(y = x\tan \theta + a\cot \theta \)
Question:The angle between the tangents drawn from the origin to the parabola \({y^2} = 4a(x - a)\) is
\({90^o}\)
\({30^o}\)
\({\tan ^{ - 1}}\frac{1}{2}\)
\({45^o}\)
Question:If line \(x = my + k\) touches the parabola \({x^2} = 4ay\), then \(k = \)
\(\frac{a}{m}\)
am
\(a{m^2}\)
\( - a{m^2}\)
Question:The equation of the common tangent touching the circle \({(x - 3)^2} + {y^2} = 9\) and the parabola \({y^2} = 4x\) above the x-axis, is
\(\sqrt 3 y = 3x + 1\)
\(\sqrt 3 y = - (x + 3)\)
\(\sqrt 3 y = x + 3\)
\(\sqrt 3 y = - (3x + 1)\)
Question:The point at which the line \(y = mx + c\) touches the parabola \({y^2} = 4ax\) is
\(\left( {\frac{a}{{{m^2}}},\;\frac{{2a}}{m}} \right)\)
\(\left( {\frac{a}{{{m^2}}},\;\frac{{ - 2a}}{m}} \right)\)
\(\left( { - \frac{a}{{{m^2}}},\;\frac{{2a}}{m}} \right)\)
\(\left( { - \frac{a}{{{m^2}}},\; - \frac{{2a}}{m}} \right)\)
Question:The equation of normal to the parabola at the point \(\left( {\frac{a}{{{m^2}}},\;\frac{{2a}}{m}} \right)\),is
\(y = {m^2}x - 2mx - a{m^3}\)
\({m^3}y = {m^2}x - 2a{m^2} - a\)
\({m^3}y = 2a{m^2} - {m^2}x + a\)
Question:If the line \(2x + y + k = 0\) is normal to the parabola \({y^2} = - 8x\), then the value of k will be
\( - 16\)
\( - 8\)
\( - 24\)
24
Question:If the normal to \({y^2} = 12x\) at (3, 6) meets the parabola again in (27, -18) and the circle on the normal chord as diameter is
\({x^2} + {y^2} + 30x + 12y - 27 = 0\)
\({x^2} + {y^2} + 30x + 12y + 27 = 0\)
\({x^2} + {y^2} - 30x - 12y - 27 = 0\)
\({x^2} + {y^2} - 30x + 12y - 27 = 0\)
Question:The length of the normal chord to the parabola \({y^2} = 4x\), which subtends right angle at the vertex is
\(6\sqrt 3 \)
\(3\sqrt 3 \)
2
1
Question:The ends of the latus rectum of the conic \({x^2} + 10x - 16y + 25 = 0\) are
(3, –4), (13, 4)
(–3, –4), (13, –4)
(3, 4), (–13, 4)
(5, –8), (–5, 8)
Question:Tangent to the parabola \(y = {x^2} + 6\) at (1, 7) touches the circle \({x^2} + {y^2} + 16x + 12y + c = 0\) at the point
(–6, –9)
(–13, –9)
(–6, –7)
(13, 7)
Question:The eccentricity of an ellipse is 2/3, latus rectum is 5 and centre is (0, 0). The equation of the ellipse is
\(\frac{{{x^2}}}{{81}} + \frac{{{y^2}}}{{45}} = 1\)
\(\frac{{4{x^2}}}{{81}} + \frac{{4{y^2}}}{{45}} = 1\)
\(\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1\)
\(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\)
Question:The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is
\({x^2} + 2{y^2} = 100\)
\({x^2} + \sqrt 2 {y^2} = 10\)
\({x^2} - 2{y^2} = 100\)
Question:The equation of the ellipse whose latus rectum is 8 and whose eccentricity is \(\frac{1}{{\sqrt 2 }}\), referred to the principal axes of coordinates, is
\(\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1\)
\(\frac{{{x^2}}}{8} + \frac{{{y^2}}}{9} = 1\)
\(\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{32}} = 1\)
\(\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{24}} = 1\)
Question:Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points, is
\(\frac{{\sqrt 5 + 1}}{2}\)
\(9{x^2} + 5{y^2} - 30y = 0\)
\(\frac{{\sqrt 5 }}{2}\)
\(\frac{{\sqrt 3 }}{2}\)
Question:The locus of a variable point whose distance from (-2, 0) is \(\frac{2}{3}\) times its distance from the line \(x = - \frac{9}{2}\), is
Hyperbola
Question:If \(P \equiv (x,\;y)\), \({F_1} \equiv (3,\;0)\), \({F_2} \equiv ( - 3,\;0)\) and \(16{x^2} + 25{y^2} = 400\), then \(P{F_1} + P{F_2}\) equals
8
6
10
12
Question:Latus rectum of ellipse \(4{x^2} + 9{y^2} - 8x - 36y + 4 = 0\) is
8/3
\(\frac{{\sqrt 5 }}{3}\)
16/3
Question:Eccentricity of the ellipse \(4{x^2} + {y^2} - 8x + 2y + 1 = 0\) is
\(1/\sqrt 3 \)
\(\sqrt 3 /2\)
\(1/2\)
Question:The length of the axes of the conic \(9{x^2} + 4{y^2} - 6x + 4y + 1 = 0\), are
\(\frac{1}{2},\;9\)
\(3,\;\frac{2}{5}\)
\(1,\;\frac{2}{3}\)
3, 2
Question:The eccentricity of the ellipse \(9{x^2} + 5{y^2} - 18x - 2y - 16 = 0\) is
1/2
3/4
Question:The locus of the point of intersection of the perpendicular tangents to the ellipse \(\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1\) is
\({x^2} + {y^2} = 9\)
\({x^2} + {y^2} = 4\)
\({x^2} + {y^2} = 13\)
\({x^2} + {y^2} = 5\)
Question:The eccentric angles of the extremities of latus recta of the ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) are given by
\({\tan ^{ - 1}}\left( { \pm \frac{{ae}}{b}} \right)\)
\({\tan ^{ - 1}}\left( { \pm \frac{{be}}{a}} \right)\)
\({\tan ^{ - 1}}\left( { \pm \frac{b}{{ae}}} \right)\)
\({\tan ^{ - 1}}\left( { \pm \frac{a}{{be}}} \right)\)
Question:If the foci of an ellipse are \(( \pm \sqrt 5 ,\,0)\) and its eccentricity is \(\frac{{\sqrt 5 }}{3}\), then the equation of the ellipse is
\(9{x^2} + 4{y^2} = 36\)
\(4{x^2} + 9{y^2} = 36\)
\(36{x^2} + 9{y^2} = 4\)
\(9{x^2} + 36{y^2} = 4\)
Question:The sum of the focal distances of any point on the conic \(\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1\) is
9
41
18
Question:The equation of the transverse and conjugate axis of the hyperbola \(16{x^2} - {y^2} + 64x + 4y + 44 = 0\) are
\(x = 2,\;y + 2 = 0\)
\(x = 2,\;y = 2\)
\(y = 2,\;x + 2 = 0\)
Question:If the length of the transverse and conjugate axes of a hyperbola be 8 and 6 respectively, then the difference focal distances of any point of the hyperbola will be
14
Question:The length of transverse axis of the parabola \(3{x^2} - 4{y^2} = 32\) is
\(\frac{{8\sqrt 2 }}{{\sqrt 3 }}\)
\(\frac{{16\sqrt 2 }}{{\sqrt 3 }}\)
\(\frac{3}{{32}}\)
\(\frac{{64}}{3}\)
Question:The directrix of the hyperbola is \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1\)
\(x = 9/\sqrt {13} \)
\(y = 9/\sqrt {13} \)
\(x = 6/\sqrt {13} \)
\(y = 6/\sqrt {13} \)
Question:The latus rectum of the hyperbola \(9{x^2} - 16{y^2} - 18x - 32y - 151 = 0\) is
\(\frac{9}{4}\)
\(\frac{3}{2}\)
\(\frac{9}{2}\)
Question:The equation of the hyperbola whose directrix is \(2x + y = 1\), focus (1, 1) and eccentricity \( = \sqrt 3 \), is
\(7{x^2} + 12xy - 2{y^2} - 2x + 4y - 7 = 0\)
\(11{x^2} + 12xy + 2{y^2} - 10x - 4y + 1 = 0\)
\(11{x^2} + 12xy + 2{y^2} - 14x - 14y + 1 = 0\)
Question:The equation of the tangent to the hyperbola \(4{y^2} = {x^2} - 1\) at the point (1, 0) is
\(x = 1\)
\(y = 1\)
\(y = 4\)
\(x = 4\)
Question:The value of m for which \(y = mx + 6\) is a tangent to the hyperbola \(\frac{{{x^2}}}{{100}} - \frac{{{y^2}}}{{49}} = 1\), is
\(\sqrt {\frac{{17}}{{20}}} \)
\(\sqrt {\frac{{20}}{{17}}} \)
\(\sqrt {\frac{3}{{20}}} \)
\(\sqrt {\frac{{20}}{3}} \)
Question:The equation of the normal to the hyperbola \(\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1\) at the point \((8,\;3\sqrt 3 )\) is
\(\sqrt 3 x + 2y = 25\)
\(x + y = 25\)
\(y + 2x = 25\)
\(2x + \sqrt 3 y = 25\)
Question:The equation of the normal at the point (6, 4) on the hyperbola \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{{16}} = 3\), is
\(3x + 8y = 50\)
\(3x - 8y = 50\)
\(8x + 3y = 50\)
\(8x - 3y = 50\)
Question:Curve \(xy = {c^2}\) is said to be
Rectangular hyperbola
Question:The reciprocal of the eccentricity of rectangular hyperbola, is
\(\frac{1}{2}\)
\(\sqrt 2 \)
\(\frac{1}{{\sqrt 2 }}\)
Question:If \(4{x^2} + p{y^2} = 45\) and \({x^2} - 4{y^2} = 5\) cut orthogonally, then the value of p is
1/9
3
Question:Find the equation of axis of the given hyperbola \(\frac{{{x^2}}}{3} - \frac{{{y^2}}}{2} = 1\) which is equally inclined to the axes
\(y = x + 1\)
\(y = x - 1\)
\(y = x + 2\)
\(y = x - 2\)