Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 137
a hyperbola are inthe points (0, ± 3) and the eccentricity is 2. Find the equa-tion of the hyperbola. 6. Show that, in terms of a and b, e has the value _ Va* + ¥ e = 7. Express b in terms of a and e. 8. Prove that two hyperbolas which have the same eccen-tricity are similar, and conversely. 9.… … Let a point P: (x, y) move offy) along a branch of the hyperbola (1) :£ _ t. — ia2 62 Fig. 7 and let this take place, for def-initeness, in the first quadrant.The slope of the line OP is MP=yOM x Since the coordinates (x, y) of P satisfy (1), it follows that b (2) and hence (3) V Vcc2 x a * x1 When…
Geometry, Analytic
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