Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 151
Ellipse, [e < 1] In interpreting equation [30], we have to remember tliate is less than unity. Placing y i= 0, we have two values ofX, corresponding to two vertices A and A, Fig. 62, namely, 2p 2p1-e -^^ 1 + e Since e < 1, Xi < 2p and Xo > 2p. Hence, the ellipse hastwo vertices lyiiKj… … Fig. 62. Then whence 2a = DA-DA,_ 2p 2p 4pe 1 —e l + e~l-e2_ 2pe_ (1) The point C, half-way between A and A, is called thecentre of the conic. Its distances, both from the directrixand from the focus, are readily found. For DC DA + AC, l + e_ 2p , 2pe ^ 2pl + e^l-e^ l-e^ HenceAlso Hence DC = FC=DC…
Geometry, Analytic
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