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Question

The locus of a point which divides the line segment joining the point (0,−1) and a point on the parabola, x2=4y, internally in the ratio 1:2, is:

A
9x212y=8
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B
4x23y=2
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C
x23y=2
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D
9x23y=2
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Solution

The correct option is A 9x212y=8
Let point P be (2t,t2) and Q be (h,k).
By section formula,
h=2t3,k=2+t23
Now, eliminating t from the above equations, we get
3k+2=(3h2)2
Replacing h and k by x and y, we get the locus of the curve as 9x212y=8

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