Previous Years Questions

MCQ (Single Correct Answer)

The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is
The vertex of the parabola x2 + 2y = 8x $$-$$ 7 is
If P(at2, 2at) be one end of a focal chord of the parabola y2 = 4ax, then the length of the chord is
The length of the common chord of the parabolas y2 = x and x2 = y is
If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is
If t is a parameter, then $$x = a\left( {t + {1 \over t}} \right)$$, $$y = b\left( {t - {1 \over t}} \right)$$ represents
The equation of the ellipse having vertices at ($$\pm$$ 5, 0) and foci ($$\pm$$ 4, 0) is
The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is
The coordinates of the focus of the parabola described parametrically by x = 5t2 + 2, y = 10t + 4 are
If t1 and t2 be the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is true?...
The vertex of the parabola y2 + 6x $$-$$ 2y + 13 = 0 is
The coordinates of a moving point P are (2t2 + 4, 4t + 6). Then its locus will be a/an
The locus of the middle points of all chords of the parabola y2 = 4ax passing through the vertex is
The point of contact of the tangent to the parabola y2 = 9x which passes through the point (4, 10) and makes an angle $$\theta$$ with the positive sid...
A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the positive direction of x-axis. If...
Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)2 = 2(x $$-$$ 4). Then the locus of mid-point of PQ is
AB is a chord of a parabola y2 = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis o...
From the point ($$-$$1, $$-$$6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is
Let the tangent and normal at any point P(at2, 2at), (a > 0), on the parabola y2 = 4ax meet the axis of the parabola at T and G respectively. Then the...
If P1P2 and P3P4 are two focal chords of the parabola y2 = 4ax then the chords P1P3 and P2P4 intersect on the...
The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}x - 12a$$ is
From a point (d, 0) three normal are drawn to the parabola y2 = x, then
The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\alpha $$ with the axis of the p...
The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. Then, the length of the latusr...
If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $$1, 0), then
Number of common tangents of y = x2 and y = $$-$$x2 + 4x $$-$$ 4 is
Let P(at2, 2at), Q, R(ar2, 2ar) be three points on a parabola y2 = 4ax. If PQ is the focal chord and PK, QR are parallel where the co-ordinates of K i...
Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P(4, $$-$$ 4) and Q(9, 6). Let R be a point on the arc of the parabola betw...
The axis of the parabola $${x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0$$ is


If the tangent to the parabola y = x(2 $$-$$ x) at the point (1, 1) intersects the parabola at P. Find the co-ordinate of P.
Prove that for all values of m, except zero the st. line $$y = mx + {a \over m}$$ touches the parabola y2 = 4ax
Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex.

MCQ (More than One Correct Answer)

Let A, B the two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of...
The area of the region lying above X-axis, and included between the circle x2 + y2 = 2ax and the parabola y2 = ax, a > 0 is...
If the tangent to $${y^2} = 4ax$$ at the point $$(a{t^2},2at)$$ where | t | > 1 is a normal to $${x^2} - {y^2} = {a^2}$$ at the point $$(a\sec \the...
The focus of the conic x2 $$-$$ 6x + 4y + 1 = 0 is
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