Plane and solid analytic geometry; an elementary textbook (1904)
Ashton, Charles Hamilton, 1866-1936 · New York, C. Scribner's Sons · leaf 209
e parabola y2= —2mx. 192 ANALYTIC GEOMETRY [Ch. XIV 28. Find the locus of the middle points of chords ofan ellipse whose poles lie on the auxiliary circle. 29. Find the locus of the intersection of two perpen-dicular lines which are tangent respectively to two con-focal ellipses. Let the equation… … y 7 T \ 72 +v. Let (a;, ?/) be their point of intersection. Then y = lxf +-VlW + b\ The elimination of Z will give a single equation in xland y. Transpose and square. y2 - 2 Ixy + ZV2 = Z2a2 + Z>2Zy24-2Zrry+ z2= a^ + V^2Adding, (1 + P)y2 + (1 + Z2>2 = ax2 + a2Z2 + b2 + V?2 Ch. XIV] PROBLEMS…
Geometry, Analytic
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