Let P be the point (1, 0) and Q be a point on the curve y 2…

Maths Conic Sections JEE (Main) / AIEEE Problems Previous Year Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Let P be the point (1, 0) and Q be a point on the curve y 2 = 8x. The locus of midpoint of PQ is

x 2 – 4y + 2 = 0

x 2 + 4y + 2 = 0

y 2 + 2x + 2 = 0

y 2 – 4x + 2 = 0

Text Solution

Verified by Experts

The correct answer is:

The coordinate of P are (1, 0). A general point Q on y 2 = 8x is (2t 2 , 4t). Midpoint of PQ is (h, k), so

2h = 2t 2 + 1 ......(i)

2k = 4t ......(ii)

⇒ t =

On putting the values of t from equation (ii) in equation (i) we get

2h = + 1

4h = k 2 + 2

Hence, the locus of (h, k) is y 2 – 4x + 2 = 0

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