Analytic geometry and principles of algebra (1913)
Ziwet, Alexander, 1853-1928, Hopkins, Louis Allen, joint author, Hedrick, E. R. (Earle Raymond), 1876-1943 · New York, The Macmillan Company · leaf 243
fa) 230 PLANE ANALYTIC GEOMETRY [XI, § 241 whence QP~ ^ sin (i sin ((3-2 a)OQ QO ~ cos2 a an expression independent of the position of the cross-sectionCO. Denoting this positive constant by A-, we find the equation if = kx{2a-x), I.e. a- {kay- which represents an ellipse, with semi-axes a, ka and… … which represents a hyperbola, withsemi-axes a, ka and center (— a, 0). 243. Limiting Cases. As the conic is an ellipse, hyperbola,or parabola according as (3 > 2 a, < 2 a, or = 2 a, it appearsthat the parabola can be regarded as the limiting case of eitheran ellipse or a hyperbola whose…
Geometry, Analytic
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