Question

If an incident ray from the point $(-1,2)$ parallel to the axis of the parabola
$y^2=4x$ strikes the parabola, then what is the equation of the reflected ray?

Answer 1

The incident ray is parallel to the x-axis, so the y-coordinate of the point will be the same as the y-coordinate of the point in the parabola at which the ray strikes.
On putting the y-coordinate as $2$ in $y^2=4x,$ we get the x-coordinate of the point at which the ray strikes.

Therefore, the incident ray from $(-1,2)$ strikes the parabola at P$(1,2).$

Also, the reflected rays pass through the focus.


The focus of this parabola is $(1,0).$

So the equation of the reflected ray is the equation of the straight line joining the points P and the focus.

Hence, the equation of the reflected ray is
$x=1.$