Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 150
ts axes, AA and BB, by a method muchlike that of Ch. VII, § 10, for the ellipse. iHE HYPERBOLA 143 \P:ix,V) Let the two circles, C and C, and the ray from 0, be drawnas before. At the point Ldraw the tangent to C, andmark the point Q where theray cuts this line. At R drawthe tangent to C and mark… … For, OR = a, OL = b, and x = OS = a sec cf>, y = LQ = b tan <£ Hence x - = secd>, a ^ = tan <£,b and since sec2 <f> — tan2 <f> — 1, it follows that tf_ £=i. a2 &- Conversely, any point (x, y) whose coordinates satisfy thisequation is seen to lead to an angle <£, for…
Geometry, Analytic
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