Ziwet, Alexander, 1853-1928, Hopkins, Louis Allen, joint author · New York, The Macmillan company · leaf 157
. 84 whence QP _sinj8sin()8-2«) OQ • QO cos« an expression independent of the position of the cross-sectionCC. Denoting this positive constant by Jc, we find the equation y^ = lcx(2 a - x), or (^T which is an ellipse, with semi-axes a,Jca, and center (a, 0). 151. Hyperbola. In the third case(Fig.… … VIII. §152] CONIC SECTIONS 147 152. Limiting Cases. The conic is an ellipse, hyperbola, orparabola according as /? > 2 a, < 2 a, or = 2 a. Hence theparabola can be regarded as the limiting case of either anellipse or a hyperbola whose center is removed to infinity. If when j8 > 2 a (Fig.…
Geometry, Analytic
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