r if {a, 13) be any point on the ellipse - + 77=1, which therefore satisfies this equation; then (-a, -/?)also satisfies this equation, and therefore is a point on 138 Analytical Geometry. the ellipse. But (a, (B), {-a,-/3) lie on the line - - ^ = 0 which passes through the origin, and are at… … Let P be the point {x, y).Then PF=e.PM=e . ^Z, = e{CZ-CX), (7 a - ex. Also PF = e. MP = e . ZX, = e{ZC+CX),(a \ Hence PF+ PF = {a -ex) + {a + ex), The Ellipse. 139 Therefore the sum of the focal distances is con-stant for all points on the ellipse, and is equal to 2a. The preceding property, FF+FF…
Geometry, Analytic
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