Abstract
Theorem . If a point be taken on the radical axis of a coaxial system of circles, and from it tangents be drawn to any circle of the system, these tangents are cut in points on a conic, by the radical axis of the circle and a given fixed point. The two points are the foci of the conic. (Fig. 1.) Let W 1 W 2 be the line of gives an ellipse as the locus of P 1 P 2 , &c, when, as in Fig, 1, S is internal to F. If S were an external point, we should have P 1 F-P 1 S = P 1 F - P 1 f 1 = radius of F = constant, and the locus of P 1 , P 2 , &c., would be a hyperbola. When F is at infinity on the radical axis, P 1 S = P 1 f 1 , and P 1 f 1 being at right angles to W 1 W 2 , the conic is a parabola, and the line of centres the directrix.
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