Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 141
nal to the{P:(xhy{) adjacent sides. It is easily seenthat the converse* of this proposi-tion is also true, and hence it issufficient for our proof to show that (2) ^ = Z^. v ; FM FM We already have simple ex-pressions for the numerators. IfP- (xi> Vi) be a point of the right-hand branch of the… … Fig. x = Xl Now, FM=OF-OM=c-x,a* and c -x = c- Xi xx Bute = ae, and so CXi -a* — a{exx -a) Thus c — x = — (exx — a), Xi * Let the student prove this proposition as an exercise. THE HYPERBOLA 135 and we arrive finally at the desired expression for FM:FM = ~{exx- a).In a similar manner it is shown…
Geometry, Analytic
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