JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q11

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MathematicsSingle correct+4 / -1Question 11 of 75

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

Answer and worked solution

Official answer: B

Perpendicular chords. With $P(t_1^2,2t_1)$ and $Q(t_2^2,2t_2)$ , $OP\perp OQ$ gives $t_1t_2=-4$ .

Midpoint. $x=\tfrac{t_1^2+t_2^2}2$ , $y=t_1+t_2$ , so
$y^2=t_1^2+t_2^2+2t_1t_2=2x-8.$

Conic. $y^2=2(x-4)$ , with latus rectum 2.

(B)

Topics:Parabola Locus

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JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 11