Plane and solid analytic geometry; an elementary textbook (1901)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's sons · leaf 119
IX CONIC SECTIONS 62. Definition and equation.—If« a point moves so thatthe numerical ratio of its distance from a fixed point to its distance from a fixed lineremains constant, its locusis called a conic. Let the fixed line betaken as the y-axis, anda perpendicular throughthe fixed point F as… … Fig. 55. (i) = (any constant) = e. But FP = ^(x-m)2+y2, and MP = x. Then (1) becomes ^—m^ + ^ oror x2 — 2 mx -f- m2 -f- y2 = e2x2, (1 - e2) ac2 - 2 nix + y1 4- m2 = 0.100 [33] Ch. IX, § 63] CONIC SECTIONS 101 This is then the general equation of a conic. The formwhich it takes in any particular…
Geometry, Analytic
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