Question

Let P be the point (1, 0) and Q a point on the locus y² = 8x. The locus of mid-point of PQ is 

(a) y² + 4x + 2 = 0

(b) y² – 4x + 2 = 0

(c) x² – 4y + 2 = 0

(d) x² + 4y + 2 = 0

Answer 1

The correct option (b) y² – 4x + 2 = 0

Explanation:

 P(1, 0). Let R(h, k) is midpoint of PQ.

∴   Q = (2h – 1, 2k)

∵ Q lines on y² = 8x ⇒ (2k)² = 8(2h – 1)

∴  4k² = 16h – 8

∴ locus of Q(h, k) is y² = [(16x – 8)/4] = 4x – 2 = 2(2x – 1)

i.e. y² – 4x + 2 = 0 is required locus.