Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 197
ting diameter, they will coin-cide in direction with the tangent at that point. Hence: Theorem VI. The tangent to an hyperbola at the end of adiameter is parallel to the conjugate diameter. 162. Pkoblem. Give7i the co-ordinates of the extremityof one diameter, to find those of either extremity of… … or 2/ and the equation of the conjugate hyperbola is hx - ay = - ab\Solving (h) and (c), we have, since b^x^ — a^y^^ = aW, (J) («) and ft 163. Theorem VII. The difference of the squares of twoconjugate semi-dia^neters is constant and equal to the differ-ence of the sqicares of the semi-axes. Proof…
Geometry, Analytic
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