﻿ A tangent and a normal are drawn at the point P(16, 16) of the parabola y2 = 16x which cut the axis of the parabola at the points A and B respectively. If the center of the circle through P, A and B is C, then angle between PC and axis of x is : Kaysons Education

# A Tangent And A Normal Are Drawn At The Point P(16, 16) Of The Parabola y2 = 16x which Cut The Axis Of The Parabola At The Points A and B respectively. If The Center Of The Circle Through P, A and B is C, Then Angle Between PC and Axis Of x is

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## Question

### Solution

Correct option is

a = 4, the point (16, 16) corresponds to (at2, 2at) for t = 2.

ty = x + at2

is tangent and y = –tx + 2at + at3 is normal. Putting y = 0, we get

A(– at2, 0) = (–16, 0), B(2a + 2t2, 0) = (24, 0)

The circle through A, B, P will be on AB as diameter as

. Hence center C is mid-point of AB is (4, 0).

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