Let be a focal chord of the parabola

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let

PQ

be a focal chord of the parabola

y^2=4ax

. The tangents to the parabola at

P

and

Q

meet at a point lying on the line

y=2x+a

, where

a>0

. If chord

PQ

subtends an angle

\theta

at the vertex, then

\tan\theta

is (1)

\frac{2}{3}\sqrt{7}

(2)

-\frac{2}{3}\sqrt{7}

(3)

\frac{2}{3}\sqrt{5}

(4)

-\frac{2}{3}\sqrt{5}