Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the center of the circle through the points P, A and B and ∠CPB=θ then a value of tanθ is

Tangent and normal are drawn at $P (16, 16)$ on the parabola $y^{2} = 16 x,$ which intersect the axis of the parabola at $A$ and $B$ , respectively. If $C$ is the center of the circle through the points $P, A$ and $B$ and $∠ C P B = θ$ then a value of $\tan θ$ is

A
4/3
B
1/2
C
2
D
3

Solution:

The equation of tangent at $P (16, 16)$ is

$x - 2 y + 16 = 0$

The equation of normal at

$P (16, 16)$ is