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

The correct option is B y24x+2=0
Let P(1,0) and Q(h,k) be a point on the locus

k2=8h

Let (α,β) be the midpoint of PQ

α=h+12,β=k+02

2α1=h,2β=k

(2β)2=8(2α1)

β2=4α2

y24x+2=0 is the locus of the midpoint PQ

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