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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

(a) `tan^(-1)(1/2)`

B

(b) `tan^(-1)2`

C

(c) `tan^(-1)(3/4)`

D

(d) `tan^(-1)(4/3)`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) By property, the center of the circle coincides with the focus of the parabola. So,

`C-=(4,0)`
`tanalpha="Slope of PC"=(16)/(12)`
`oralpha=tan^(-1)((4)/(3))`
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