Plane and solid analytic geometry; an elementary textbook . Fig. 66. An hyperbola may be traced in the following mannerFix one end of a ruler atone focus, F. A stringwhose length is 2 a less thanthe length of the ruler isattached to the focus F andto the other end of the pencil, which holds thestring taut and against the ruler, will trace a branch ofthe hyperbola. For in all positions of P, FP -FP=2a. The parabola is per-haps more easily tracedby points. Erect a per-pendicular ML at anypoint of the axis. WithF as a centre and a radiusequal to DM, describe anarc, cutting ML at P
Plane and solid analytic geometry; an elementary textbook . Fig. 66. An hyperbola may be traced in the following mannerFix one end of a ruler atone focus, F. A stringwhose length is 2 a less thanthe length of the ruler isattached to the focus F andto the other end of the pencil, which holds thestring taut and against the ruler, will trace a branch ofthe hyperbola. For in all positions of P, FP -FP=2a. The parabola is per-haps more easily tracedby points. Erect a per-pendicular ML at anypoint of the axis. WithF as a centre and a radiusequal to DM, describe anarc, cutting ML at P is a point of theparabola. For JSTP = many points as we please may be found in this way and the parabola passed through them. 72. Auxiliary circles. — The auxiliary circle of a cen-tral conic is a circle described on the major axis asdiameter. Its equation is x2 + y2 = a2. The circle described on the minor axis as diameteris called the minor auxiliary circle. Its equation isx2 -f y2 = Fig. 67. 122 ANALYTIC GEOMETRY [Ch. IX, § 72 Points on the ellipse and auxiliary circle which havethe same abscissa are called corresponding points. In
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