Question

If a ray of light along the line $y=4$ gets reflected from a parabolic mirror whose equation is $(y-2{)}^2=4(x+1)$, then equation of reflected ray will be

Answer 1

As we know that any line which is moving parallel to axis of parabola after get reflected by the parabola passes through the focus of the parabola.
For the given parabola focus will be
$S(0,2)$
Now let the ray of light meet the parabola at $P$ then
$(4-2{)}^2=4(x+1)\Rightarrow x=0$
Hence $P(0,4)$
So equation of the reflected ray will be line passing through $P$ and $S$ i.e., $x=0$