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Question

If two tangents drawn from the point (α,β) to the parabola y2=4x such that the slope of one tangent is double of the other, then

A
β=29α2
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B
α=29β2
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C
2α=9β2
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D
α=2β2
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Solution

The correct option is B α=29β2
For y2=4x, let tangent equation be
y=mx+amy=mx+1m
Tangent passes through (α,β)
β=mα+1m
αm2βm+1=0

Let the slope of one tangent be m,
Therefore, slope of other tangent is 2m
m+2m=βα3m=βαm=β3α(i)2m×m=1α2m2=1α
Using equation (1), we get
2(β29α2)=1αβ2=9α2α=2β29

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