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If a line y=3x+1 cuts the parabola x^2-4...

If a line `y=3x+1` cuts the parabola `x^2-4x-4y+20=0` at `A and B ,` then the tangent of the angle subtended by line segment `A B` at the origin is

A

`8sqrt(3)//205`

B

`8sqrt(3)//209`

C

`8sqrt(3)//215`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2) The joint equation of OA and OB is
`x^(2)-4x(y-3x)-4y(y-3x)+20(y-3x)^(2)=0`
(Making the equation of the parabola homogeneous using straight line)
`or193x^(2)+16y^(2)-112xy=0`
`tantheta=(2sqrt(h^(2)-ab))/(a+b)`
`=(2sqrt(56^(2)-193xx16))/(193+16)`
`=(8sqrt(3))/(209)`
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