Analytic geometry for colleges, universities, and technical schools (1892)
Nichols, E. W. (Edward West), 1858- · Boston [Mass.] : Leach, Shewell & Sanborn · leaf 147
t ^ + 2^ = 1. a ^ b^ hence, a^ _|_ ^2 ^ ^2 _|_ ^2 _ _ _ (^4^) 98. To show that the parallelogram constructed on any tivoconjugate diameters is equivalent to the rectangle constructedon the axes. Let PR ( = 2a), FR ( = 2b), Pig. 44, be any two conju-gate diameters. To prove that area CTCT = area… … From the triangles ODP, ODP, we have DP y hx . a— -^^ — • sm Q sm (jD = OD OP y ah COS QD := = = OP b ail /, X —^ : cos Q =—- hV a Hence sin (qp — ^) = sin go cos 0 — cos (jd sin B ay- hx aah lah aabb aWabab ab THE ELLIPSE. 133 Substituting this value in (1) and multiplying through by 4, we have…
Geometry, Analytic
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