So let's say you have a curved mirror, $y=y(x)$ with this property: Whenever a ray of light emanates from the origin, it reflects parallel to the x axis.
Find the equation of the mirror.
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Making Ross's answer more explicit: remember that in the vicinity of the point where the light ray from the origin strikes your mirror, you can replace the curved mirror with the corresponding tangent line. Try deriving a differential equation for your $f(x)$ (hint: you may have to use the formula for the tangent of the difference of two angles) such that the reflected ray has zero slope (i.e., is horizontal).