Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 190
l does to the axis of X,we may obtain the equation of the former from that of thelatter by simply interchanging the quantities which relate tothe two axes. Thus if the equation of the original hyper-bola is bx - ay = ab\ then, by interchanging X and y,a and b, we have, after changing signs, JV - ay… … Let the angle AFF = 6 and PF = r be the polar co-ordinates of any point P. Then we shall have PF = PF + FF - 2PF\ FF cos FFP,or PF = r= + 4fte^ - 4aer cos 6,Now, by the fundamental property of the curve, we havePF- PF ^^a, or ^v + ^ae whence we get r 4iaer cos 6 — r = 2a;a(e - 1) (12) 1 -i- e cos…
Geometry, Analytic
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