Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 221
intersects that tangent on the circle described with the centreof the ellipse as a centre and the major axis as a diameter. 100. Equation of a Diameter. We have already defined a diameter of a conic as the locusof the middle points of a system of parallel chords. To findthe equation of a diameter,… … Fig. 91. If X3 and ya be the coordinates of the middle point of thechord, then xi -f- X2 X3 2 yi + y2 THE ELLIPSE. 207 But Xi and Xo are the roots of the equation (b^ + a-mr) x2 + 2a-miCx + a (c- - b^) = 0;so that xand hence Similarly, whence, by division, Xg a-irii This equation is satisfied by…
Geometry, Analytic
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