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Question

Let PQ be a focal chord of parabola y2=x. If the coordinates of P is (4,2), then the slope of the tangent at Q is

A
8
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B
4
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C
18
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D
4
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Solution

The correct option is D 4
Given parabola is y2=x
Any point on the parabola is (t24,t2)
Comparing with the coordinates of P(t),
(t24,t2)=(4,2)t=4
As PQ is focal chord, so coordinates of Q(1t) is (14t2,12t)=(164,18)

Now, equation of tangent at Q is T=0
y×18=12(x+164)y=4x+116
Hence, the slope of the tangent at Q is 4.

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