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Question

If one vertex of a chord of parabola y2=8ax is at (0,0), then the locus of a point which divides the chord in the ratio 1:2 is

A
y2=4ax
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B
y2=8ax
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C
y2=8a3x
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D
y2=2ax
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Solution

The correct option is C y2=8a3x
Let the point be P(h,k) and other end point of chord on the parabola be Q(x,y)
Then h=x+02+1
x=3h
and k=y+02+1
y=3k

Since (x,y) lies on y2=8ax,
(3k)2=8a×3h
k2=8a3h
Hence, locus of the point P is y2=8a3x which is a parabola.

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