The vertex of the parabola | parabola | JEE MAIN 2026

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JEE MAIN 2026

08-04-2026_S2

Question

Let $O$ be the vertex of the parabola $y^2=4 x$ and its chords $O P$ and $O Q$ are perpendicular to each other. If the locus of the mid-point of the line segment $P Q$ is a conic $C$, then the length of its latus rectum is :

Select the correct option:

A

1

B

2

C

4

D

8

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & t_1 t_2=-4 \\ & 2 h=t_1^2+t_2^2 \quad 2 k=2\left(t_1+t_2\right)\end{aligned}$
$\begin{aligned} & 2 h=k^2-2 t_1 t_2 \\ & 2 h=k^2+8 \\ & k^2=2 h-8 \\ & =2((h-4) \\ & \text { L.R. }=2\end{aligned}$

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