Reflection from a parabolic mirror

A parabolic mirror $4Fx = y^2$ intersects the optical axis at $(x=0,y=0)$. The mirror has a focus $F$. For $F>0$ the interface is convex and for $F<0$ the interface is concave. Light rays leave an object $o$ and are reflected by the mirror.

If a point light source is , the reflected light rays will be parallel. This is used in spotlights and car headlights.

Parabolic mirrors are used to concentrate parallel light rays and focus them at the focus of the parabola. This is used in reflecting telescopes, solar furnaces, and satelite dishes.