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Question

Tangents are drawn from the points on the parabola y2=8(x+4) to the parabola y2=4x. Then the locus of mid-point of chord of contact of y2=4x is

A
5y2=8(x+4)
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B
5y2=4(x4)
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C
5y2=8(x4)
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D
5y2=4(x+4)
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Solution

The correct option is C 5y2=8(x4)
Let (x1,y1) be point on y2=8(x+4).
Then equation of chord of contact is T=0
i.e., 2xy1y+2x1=0 (1)

Let P(h,k) be its mid-point.
Then its equation will be
T=S1
2xky+2h=k24h
2xky+k22h=0 (2)

Comparing (1) and (2), we get
k=y1, 2x1=k22h
So, k2=4(k22h+8)
k2=85(h4)
Hence, locus of mid-point of chord of contact is 5y2=8(x4)

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