Question

If the normal to a parabola $y^{2}=4 a x$ at $P$ meets the curve again in $Q$ and if $P Q$ and the normal at $Q$ make angles $\alpha$ and $\beta$, respectively with the $x$-axis, then $\mid \tan \alpha(\tan \alpha+$ $\tan \beta)$ has the value equal to

Answer 1

$\tan \alpha=-t_{1}$ and $\tan \beta=-t_{2}$
also $t_{2}=-t_{1}-\frac{2}{t_{1}}$

$t_{1} t_{2}+t_{1}^{2}=-2$
$\tan \alpha \tan \beta+\tan ^{2} \alpha=-2 \Rightarrow (B)$.