2019-06-14 13:43:16 UTC
"If we slice through a cone, depending on the angle of the cut, the edges will form a circle, ellipse, parabola, or hyperbola (figure 1). On this page, we'll discuss the shape each cut appears to have, simply from an inspection of the cone and the way the lines pass through it, and then we'll use a little algebra to prove that the sections really do have the claimed forms.
"Note that each of the conic sections has its own "focus property", different for each. The focus properties are shown pictorially on our parabola focus, ellipse focus, and hyperbola focus pages, where we also derive equations for each of those figures starting with the definitions."