### JEE Main On 08 April 2018 Question 13

##### Question: Tangent and normal are drawn at $ p(16,16) $ on the parabola $ y^{2}=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 $ \angle CPB=\theta $ , then a value of tan $ \theta $ is: [JEE Main Online 08-04-2018]

#### Options:

A) 3

B) $ \frac{4}{3} $

C) $ \frac{1}{2} $

D) 2

## Show Answer

#### Answer:

Correct Answer: D

#### Solution:

$ A(-16,0) $ $ B(16+2(4),0)=B(24,0) $

$ AC=CB\Rightarrow C(4,0) $

C is the cimcumcentre $ BP=\sqrt{8^{2}+16^{2}}=8\sqrt{5} $

$ PC=\sqrt{12^{2}+16^{2}}=20 $

$ \Rightarrow \tan \theta =2 $