Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 149
equa-tion of the hyperbola. w,/ - 7^. Jb s r i 6. Show that, in terms of a and h, e has the value -^ ■VaF+¥e = —• a f. Express b in terms of a and e. 8. Prove that two hyperbolas which have the same eccen-tricity are similar, and conversely. 9. Establish formulas (3). y f . H 4. The Asymptotes. Two… … Let a point P: (x, y) move offalong a branch of the hyperbola (1) a ^ _ 2/^ _ 1 Fig. 7 and let this take place, for def-initeness, in the tirst quadrant.The slope of the line OP is MP ^yOM X Since the coordinates (a;, y) of P satisfy (1), it follows that h (2) and hence (3) y =- Va;2 — a^,a…
