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Parabola

305 Questions Start JEE Mains Test
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1994 Q301 JEE Advanced Numerical
14 Mar 2026
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 $PQ$.
1994 Q302 JEE Advanced Numerical
14 Mar 2026
The point of intersection of the tangents at the ends of the latus rectum of the parabola ${y^2} = 4x$ is ...... .
1991 Q303 JEE Advanced Numerical
14 Mar 2026
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 Q304 JEE Advanced Numerical
14 Mar 2026
$A$ 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 Q305 JEE Advanced Numerical
14 Mar 2026
Suppose that the normals drawn at three different points on the parabola ${y^2} = 4x$ pass through the point $(h, k)$. Show that $h>2$.