H. S. MacDonald Coxeter - Whence does an ellipse look like a circle?

In Euclidean 3-space, a system of confocal quadric contains two degenerate members: a focal ellipse and a focal hyperbola, lying in perpendicular planes in such a way that the foci of each coincide with the vertices of the other. George Salmon discovered that, when viewed from any point on the focal hyperbola, the focal ellipse looks like a circle! It seems worth while, quite apart from the consideration of quadrics, to give an elementary solution to the problem of finding the locus of viewpoints from which a given ellipse looks like a circle (and later, of finding the two viewpoints from which every plane section of a prolate spheroid looks like a circle).