Question

Let $P_{1}$ be a parabola with vertex $(3,2)$ and focus $(4,4)$ and $P_{2}$ be its mirror image with respect to the line $x +2 y =6$. Then the directrix of $P _{2}$ is $x +2 y =$ ______.

Answer 1

$P_{1}: $ Directorix :
$ x +2 y = k $
$ x +2 y - k =0 $
$\left|\frac{3+4- K }{\sqrt{5}}\right|=\sqrt{5} $
$|7- k |=5 $