Question

Two tangent lines l 1 and l 2 are drawn from the point (2, 0) to the parabola 2 y 2 = – x. If the lines l 1 and l 2 are also tangent to the circle (x – 5)2 + y 2 = r , then 17 r is equal to _________.

Answer 1

$y² = -\frac{x}{2}$
$y = mx - \frac{1}{8m}$
this tangent pass through (2, 0)

$\begin{array}{l}\Rightarrow m=\pm \frac{1}{4}\end{array}$i.e. one tangent is
$x-4y-2=0$
$17r = 9$