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Tangent and normal are drawn at P(16,16)...

Tangent and normal are drawn at P(16,16) on the parabola `y^2=16x` which intersect the axis of the parabola at A and B respectively. If C is the centre of the circle through the points P,A and B and `angle CPB=theta` then the value of `tan theta` 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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