JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Parabola

Let O be the vertex of the parabola

y^{2} = 4 x

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 :

(A)1
(B)2✓ Correct
(C)4
(D)8

Answer: (B)

Solution

Take

P (t_{1}^{2}, 2 t_{1})

and

Q (t_{2}^{2}, 2 t_{2})

y^{2} = 4 x

. The chords

O P

and

O Q

have slopes

\frac{2}{t _{1}}

and

\frac{2}{t _{2}}

, and perpendicularity gives

\frac{4}{t _{1} t _{2}} = - 1

, so

t_{1} t_{2} = - 4

. For the midpoint

(h, k)

P Q

k = t_{1} + t_{2}, 2 h = t_{1}^{2} + t_{2}^{2} = (t_{1} + t_{2})^{2} - 2 t_{1} t_{2} = k^{2} + 8.

Hence

k^{2} = 2 h - 8 = 2 (h - 4)

, a parabola whose latus rectum has length

2

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option

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