Let $P Q$ be a focal chord of the parabola $y^{2}=4 a x$. The tangents to the parabola at $P$ and $Q

Question

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 the chord $P Q$ is\

Professor PC Thomas Classes · Answer

(b) :\ $\left(-a, a\left(t-\frac{1}{\mathrm{t}}ight)ight)$\ Given $a\left(t-\frac{1}{t}ight)=-a . \quad 	herefore t-\frac{1}{t}=-1$\ $P Q=a\left(t+\frac{1}{t}ight)^{2}=a\left\{\left(t-\frac{1}{t}ight)^{2}+4ight\}=5 a$\