There are three types of conics&colon; the ellipse, parabola, and hyperbola. Generalized conics with three foci are called trifocal ellipses. In this case, one talks of "conic sections", or "conics". A pencil of conics can represented algebraically in the following way. This proof proves the theorem for circle and then generalizes it to conics. Equivalently again, both sheets of the focal surface degenerate to conics. All these degenerate conics may occur in pencils of conics. This had the effect of reducing the geometrical problems of conics to problems in algebra. Classical conics can be realized as equidistant sets. The formal extension of the concept of confocal conics to surfaces leads to confocal quadrics. This concept is useful when considering degenerate conics, which may include the cylindrical conics. This is useful in the definition of degenerate conics, which require considering the cylindrical conics. All of these non-degenerate conics have, in common, the origin as a vertex (see diagram). The simplest way to explore lunar transfer trajectories is by the method of patched conics. The level sets formula 17 are called generalized conics.