Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 128
he equation of the line simultaneously. T7ie circle. Let the given curve be the circle X- + y = a^, and take the equation of the line in the slope form y = mx + k. Eliminating y between (1) and (2),we see that the .^-coordinates of thepoints of intersection are the rootsof the equation (1 + »n-2)x2… … Fig. 70 that is, when 4 (1 + vi) {k~ - a2) = 4 m^ 112 LOCI OF SECOND ORDER [Chap. VII. Solving this equation for k, we have A; = ± a Vl + m^ Hence, when Ti has either of these vahies, the roots of (A) areequal and the points of intersection of the circle with the linecoincide. Therefore, the lines…
Geometry, Analytic
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