Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 184
turned in the opposite direction. Thus we see that the com-plete curve consists of two branches, as represented above. 150. Problem. To find the equation of the hyperlola. Let tlie straight line drawnthrough the foci ^e takenas the axis of X; t. * pointC midivay between tj iocibe taken as the… … and therefore FM ^ x-^-c,FM =x-c, (1) ^^ = (^ + ^r + !/; PF^={x-cY^y^,and, by the fundamental property of the curve, V(^ + cf 4- y - f (:,• - cy + y = 2a.Freeing this equation of surds, we have (c - a)x - ay = a\c - a),which is the required equation. This, however, may be simplified by putting, for…
Geometry, Analytic
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