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 `Aa n dB` , rerspectively. If the center of the circle through `P ,A ,a n dB` is `C` , then the angle between `P C` and the axis of `x` is `tan^(-1)1/2` (b) `tan^(-1)2` `tan^(-1)3/4` (d) `tan^(-1)4/3`

Options

A. `tan^(-1)(1)/(2)`
B. `tan^(-1)2`
C. `tan^(-1)(3)/(4)`
D. `tan^(-1)(4)/(3)`

Answer

D

Explanation

(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))`