Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 199
ve 4:ab sin (p = 4^5 = a constant, (19) which proves the proposition. THE HYPERBOLA. 183 166. Problem. To find the equation of the hyperholareferred to a2)air ofcovjvgatediameters as axes. Let DD, HH be any pairof conjugate diameters. TakeDD for the new axis of X,and HH for the new axis ofYy and… … {a shia - b cosa)x-{- {a shi/3- b cos/3)y ab\ (20) which is the equation required. By putting x and y each equal to zero, we get the inter-cepts on the axes or the lengths of the semi-conjugates.Thus, when y = 0, x = — ab = CD = a; a sii] ia — b cos a and when x = 0, we have / — aW i ~ - CH = ^,2c…
Geometry, Analytic
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