Let PQ be a focal chord of the parabola `y^(2)=4ax`. The tangents to the parabola at P and Q meet at point lying on the line
`y=2x+a,alt0`.
If chord PQ subtends an angle `theta` at the vertex of `y^(2)=4ax`, then `tantheta=`

Options

A. `(2)/(3) sqrt(7)`
B. `(-2)/(3) sqrt(7)`
C. `(2)/(3) sqrt(5)`
D. `(-2)/(3) sqrt(5)`

Answer

D

Explanation

`m_(OP) = (2at - 0)/(at^(2) - 0) = (2)/(t)`

`m_(OQ) = (-2a//t)/(a//t^(2)) = - 2t`
`:. Tan theta = ((2)/(t) + 2t)/(1 - (2)/(t).2t) = (2(t - (1)/(t)))/(1 - 4) = (-2 sqrt(5))/(3)`
Where `t + (1)/() = sqrt(5)`