A Hyperbola has an interesting property: any ray cast from one of its focal points will be reflected in such a way that it appears to originate from the other focal point.
In the image below this means an observer (in the top right corner) looking in the direction of F2 would actually always see the mirror image of F1. The reason behind this is that the tangent in any point of a hyperbola will always be the angle bisector of the two lines leading towards the focal points.