Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 153
thef \ ^^^i-(ai, yi) adjacent sides. It is easily seen that the converse * of this proposi-tion is also true, and hence it issufficient for our proof to show that ^ ^ FM Fm Pjq We already have simple ex- pressions for the numerators. If-P- (^1) 2/i) t)e a point of the right-hand branch of the… … Now, and But c = ae, and so Xi FM= OF- OM=c- x\ , a^ cXi — a^c — x = c = — a-l X, cxi — a^ = a{exi— a).Thus c — x = ~ (exi — 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=^{ex,-a).In a similar manner it…
