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Let P be the point (1, 0) and Q be a poi...

Let `P` be the point (1, 0) and `Q` be a point on the locus `y^2=8x` . The locus of the midpoint of `P Q` is (a) `y^2+4x+2=0` (b) `y^2-4x+2=0` (c) `x^2-4y+2=0` (d) `x^2+4y+2=0`

A

`y^(2)+4x+2=0`

B

`y^(2)-4x+2=0`

C

`x^(2)-4y+2=0`

D

`x^(2)+4y+2=0`

Text Solution

Verified by Experts

The correct Answer is:
B
(2) Let R (h,k) be the midpoint of PQ. Therefore, Q is (2h-1,2k)
Since Q lies on `y^(2)=8x`, we get
Hence, the locus of Q (h,k) is
`y^(2)=2(2x-1)`
`or" "y^(2)=4x-2`
`or" "y^(2)-4x+2=0`
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