405. Mechanical means of describing hyperbolas, their foci and vertices being given. Suppose the curves two opposite hyperbolas, the points in vertical dotted center line their foci. One end of rule turns on one focus as a center through which one edge ranges. One end of thread being looped on pin inserted at the other focus, and other end held to other end of rule, with just enough slack between to permit height to reach vortex when rule coincides with center line. A pencil held in bight, and kept close to rule while latter is moved from center line, describes one-half of parabola; the rule is then reversed for the other half.