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Question

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

A
y24x+2=0
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B
y2+4x+2=0
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C
x2+4y+2=0
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D
x24y+2=0
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Solution

The correct option is A y24x+2=0
P=(1,0),Q=(h,k)

k2=8h

Let (α,β) be the mid-point of PQ.

α=h+12,β=k+02

2α1=h,2β=k

(2β)2=8(2α1)

β2=4α2

y24x+2=0

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