Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 151
it will be tangent to M. Let the pointof tangency be denoted by F, and the circle of contact of thesphere with the cone by C. Through an arbitrary point P of the curve of intersection ofM with the cone passes a generator OP of the cone ; let it cutC in R and C in R. Then RR> being the slant… … Fig. 15 THE HYPERBOLA 145 the frustum * cut from the cone by the planes of C and C-, isof the same length, 2 a, for all points P. Join P with F. Then PF and PR, being tangents from Pto the same sphere, are equal. Similarly, PF and PR areequal. Hence FP + FP =RP+ RP= RR,or FP+FP = 2a. But this locus…
Geometry, Analytic
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