If P 1 Q 1 and P 2 Q 2 are two focal chords of the parabola…

Maths Conic Sections General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If P 1 Q 1 and P 2 Q 2 are two focal chords of the parabola y 2 = 4ax. then the chords P 1 P 2 and Q 1 Q 2 intersect on

tangent at the vertex of the parabola

the directrix of the parabola

at x = –2a

y = 2a and x = –2a

Text Solution

Verified by Experts

The correct answer is:

Let co-ordinate of P 1 and P 2 be and then co-ordinate of Q 1 and Q 2 are

and respectively. (  P 1 Q 1 and P 2 Q 2 are focal chords)

∴ Equation of P 1 P 2 is

y(t 1 + t 2 ) = 2(x + at 1 t 2 ) ...(i)

replacing t 1 by – 1/t then euation of Q 1 Q 2 is

⇒ –y(t 1 + t 2 ) = 2(x t 1 t 2 + a) ...(ii)

adding (i) & (ii) we get

0 = 2(1 + t 1 t 2 )(x + a)

2(1 + t 1 t 2 ) ≠ 0

x + a = 0

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