Parabola PYQs - Last 5 Years

The parabola $y=4-x^2$ has vertex P. It intersects $x$-axis at A and B. If the parabola is translated from its initial position to a new position by moving its vertex along the line $y=x+4$, so that it intersects $x$-axis at B and C , then ...

If the locus of mid point of any normal chord of the parabola $y^2=4 x$ is $x-\lambda=\frac{\mu}{y^2}+\frac{y^2}{v}$, where $\lambda, \mu, v \in N$, then ( $\lambda+\mu+v$ ) equals to

The line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at the points $P$ and $Q$. If the co-ordinates of the point $X$ are $(\sqrt{3}, 0)$, then the value of $X P \cdot X Q$ is

\(\triangle \mathrm{OAB}\) is an equilateral triangle inscribed in the parabola \(\mathrm{y}^2=4 \mathrm{a} x, \mathrm{a}>0\) with O as the vertex, then the length of the side of \(\triangle \mathrm{O A B}\) is

From the focus of the parabola \({y^2} = 12x\), a ray of light is directed in a direction making an angle \({\tan ^{ - 1}}{3 \over 4}\) with x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

Let O be the vertex, Q be any point on the parabola x\(^2\) = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpendicular bisector of AB meet the y-axis M. Let N be the midpoint of LM. Then locus of N is

If P1P2 and P3P4 are two focal chords of the parabola y2 = 4ax then the chords P1P3 and P2P4 intersect on the

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 radius of the circle through P, T and G is

From the point (\(-\)1, \(-\)6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents 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 of the parabola is

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

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 this line meets the curve \({x^2} = 4y - 9\) at A and B, then |AB| is equal to

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 side of the axis of the parabola where tan\(\theta\) > 2, is