Mathematics for engineering students, Analytical geometry and calculus (1907)
Keller, S. S. (Samuel Smith), 1867-1923, Knox, W. F., [from old catalog] joint author · New York : D. Van Nostrand company · leaf 129
and y will be the co-ordinates of the points ofintersection, R and S.• Substituting the value of y from (1) in the ellipse equation, a2 ( ~ f *X\2 + b2 x2 = a2 b2,\ a2yr J + b2x2= a2 b2, b4x2x2 ,2 A/2 a yb2 x2 (b2 x2 + a2 y2) =aH2 a2y2b2x2(a2b2) = 2a2/2 [Since b2 xf2 + a2 y2 = a2 b2,point (x, /)… … R being the extremities of conjugate diameters. (Fig. 46.)Then if (OT, RT) are (- xf, /), (OT, RT) are In the right triangles ORT and ORT OR2 = OT2 + RT2 = x2 + y\ b2x2 andOR,2=OT,2 + R,T/2 a2ynb2 Then OR2 + OR x/2 + a2/2 + y2 + b2 x2 _ b2 x2 + a2 y2 a2 y2 + b2 x2 b2 a2 a2 b2 ^a2b2 \ , h2= —— + =a2…
Geometry, Analytic · Calculus
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