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Tangent and normal are drawn at the poin...

Tangent and normal are drawn at the point `P-=(16 ,16)` of the parabola `y^2=16 x` 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 the angle between `P C` and the axis of `x` is

A

`4//3`

B

`1//2`

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
3 Given parabola is `y^(2)=16x`.

Equation of tangent at point P(16,16) is
`16y=8(x+16)or2y=x+16`
It meets x-axis at A(-16,0).
Slope of normal is -2.
Equation of normal at P is
y-16=-2(x-16) of 2x+y=48
It meets x-axis at B(24,0).
Circumcircle of triangle APB has center C at mid-point of AB.
`:." "C-=(4,0)`
Slope of CP `=(16)/(12)=(4)/(3)`
`:." "tantheta=|((4)/(3)-(-2))/(1+(4)/(3)(-2))|=|(10)/(-5)|=2`
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