Plane and solid analytic geometry; an elementary textbook (1901)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's sons · leaf 162
between these two points. 142 Ch. XI, § 79] DIAMETERS 143 Starting the solution of the two equations, y = l1x + ftand b2x2 + a2y2 = a2b2* we have Q>2 + a\2) x2 + 2 a%#r + a2 (ft2 - I2) = 0, the two roots of which must be xx and x2. But Hence a\ft [By Art. 8] b2 + fl2^2 Since (V, «/) is on the… … Fig. 78. 144 ANALYTIC GEOMETRY [Ch. XI, § 80 Let the student show that the equation of a diameter oi the hyperbola, —^ - &- = 1, is Woe - a*hy = 0, [61] the parabola, y2 = 2 mx, is hy = m. [62] TAe /orm of the equation of a diameter of an ellipse orhyperbola shows that it passes through the…
Geometry, Analytic
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