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Question

Let P be the point (1,0) and Q be a point on the curve y2=8x. Then the locus of the 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 R(h,k) be the mid-point of PQ.
By mid-point formula,
Q is (2h1,2k)


Since Q lies on y2=8x,
(2k)2=8(2h1)
k2=2(2h1)
Hence, locus of Q is
y2=2(2x1)
y24x+2=0

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