Let $P Q$ be a focal chord of $y^{2} = 4 a x$ . The tangents to parabola at $P$ and $Q$ meet at a point lying on the line $y = 2 x + a (a > 0)$ . If the chord $P Q$ subtends an angle $θ$ at the vertex of prabola then $tan θ =$

Q. Let

P Q

be a focal chord of

y^{2} = 4 a x

. The tangents to parabola at

P

and

Q

meet at a point lying on the line

y = 2 x + a (a > 0)

. If the chord

P Q

subtends an angle

θ

at the vertex of prabola then

tan θ =

Q. Let

P Q

be a focal chord of the parabola

y^{2} = 4 a x

. The tangents to the parabola at

P

and

Q

meet at a point lying on the line

y = 2 x + a, a > 0

.
Length of chord

P Q

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Let PQ be a focal chord of the parabola y2=4ax. The tangents to the parabola at P and Q meet at a point lying on the line y=2x+a,a>0. If chord PQ subtends an angle θ at the vertex of y2=4ax, then tan θ is equal to

The correct option is D −23√5 mOP=2at−0at2−0=2t mOQ=−2atat2=−2t∴tanθ=2t+2t1−2t.2t=2(t+1t)1−4 where t+1t=√5 =2√5−3

Let $P Q$ be a focal chord of the parabola $y^{2} = 4 a x$ . The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y = 2 x + a, a > 0$ .
If chord $P Q$ subtends an angle $θ$ at the vertex of $y^{2} = 4 a x$ , then tan $θ$ is equal to