JEE Main | 2018CircleHard

Question

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tanθ is

Options

A.

2

B.

3

C.

4/3

D.

1/2

Solution


Equation of tangent at P(16, 16)
is x - 2y + 16 = 0
mPC = 4/3
mPB = - 2
Hence, tan θ = mPC-mPB1+mPC . mPB
tan θ = 2

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