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Question

Let O be the vertex and Q be any point on the parabola, x2=8y. If the point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is

A
x2=y
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B
y2=x
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C
y2=2x
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D
x2=2y
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Solution

The correct option is B x2=2y
Vertex of the parabola x2=8y is O(0,0)

And any point on the parabola is Q(4t,2t2)

Let P(h,k) divides the line segment OQ internally in the ratio 1:3

h=3×0+1×4t1+3=t

and k=3×0+1×2t21+3=t22

Eliminating t we get, h2=2k

Hence the locus of p(h,k) is, x2=2y

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