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Parabola

208 Questions
All Exams JEE Mains JEE Advanced
1996 JEE Advanced Numerical
IIT-JEE 1996
Points $A, B$ and $C$ lie on the parabola ${y^2} = 4ax$. The tangents to the parabola at $A, B$ and $C$, taken in pairs, intersect at points $P, Q$ and $R$. Determine the ratio of the areas of the triangles $ABC$ and $PQR$.
1996 JEE Advanced Numerical
IIT-JEE 1996
From a point $A$ common tangents are drawn to the circle ${x^2} + {y^2} = {a^2}/2$ and parabola ${y^2} = 4ax$. Find the area of the quadrilateral formed by the common tangents, the chord of contact of the circle and the chord of contact of the parabola.
1995 JEE Advanced Numerical
IIT-JEE 1995
Show that the locus of a point that divides a chord of slope $2$ of the parabola ${y^2} = 4x$ internally in the ratio $1:2$ is a parabola. Find the vertex of this parabola.
1994 JEE Advanced Numerical
IIT-JEE 1994
Through the vertex $O$ of parabola ${y^2} = 4x$, chords $OP$ and $OQ$ are drawn at right angles to one another . Show that for all positions of $P$, $PQ$ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of $PQ$.
1991 JEE Advanced Numerical
IIT-JEE 1991
Three normals are drawn from the point $(c, 0)$ to the curve ${y^2} = x.$ Show that $c$ must be greater than $1/2$. One normal is always the $x$-axis. Find $c$ for which the other two normals are perpendicular to each other.
1982 JEE Advanced Numerical
IIT-JEE 1982
$A$ is point on the parabola ${y^2} = 4ax$. The normal at $A$ cuts the parabola again at point $B$. If $AB$ subtends a right angle at the vertex of the parabola. Find the slope of $AB$.
1981 JEE Advanced Numerical
IIT-JEE 1981
Suppose that the normals drawn at three different points on the parabola ${y^2} = 4x$ pass through the point $(h, k)$. Show that $h>2$.
1994 JEE Advanced Numerical
IIT-JEE 1994
The point of intersection of the tangents at the ends of the latus rectum of the parabola ${y^2} = 4x$ is ...... .