t (^, y). The equation of any straight line through the point(x\ y) is A{x-x) + B{y-y) = 0. ...(1) If this be the normal at {x, y) it is perpendicularto the tangent and the condition of perpendicularity (§ 25) is -3.A + |(.5 = 0 (2) a^ b- ^ ^ 146 Analytical Geometky. Introducing in (1) tlie… … Let the normal at P cut the axis major in G. Thenthe co-ordinates of G are CG and 0. Substitutingthese in the equation of the normal (§ 73), t^.CG--,.O^o--ly; The Ellipse. 147 a- Hence FG = ae + e~x, and GF= ae - e-x. . FG_ae + €^x a + ex_FP^ GF ~ae-e%~a-ex~ FF and therefore FG, the normar, bisects…
Geometry, Analytic
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