Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 158
to the sum of thesquares of the semi-axes. Proof Let (x, «/) be the co-ordinates of P (last figure),and denote the semi-conjugate axes CP, CD by a and brespectively. Then we shall have CP» + CD^ = x^ + 2/ + ^y-- + l^;- _ab aW~ b ^ a or a + b = a-\- b\ (9) 12*7. Problem. To find the angle between… … Denote the semi-conjugate axes by a and b, and the co-ordinates of P by x, y. Then (§ 125) the co-ordinates of Dare -p +^• Hence sin Q = ^-; cos u = —,-; • af ^^ cos^= ,,- Substituting in (a), we have bx ,^ ^ = aab + THE ELLIPSE. 143 (10) But since (?/, y) is on the curve, Therefore sm a> = ,…
Geometry, Analytic
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