Tanner, J. H. (John Henry), b. 1861, Allen, Joseph · New York, American Book Co · leaf 212
chords whose slope is m. Clearly, if the axes are equal, so that b = a, the curve takesthe special form of the circle, with eccentricity e = 0, the twofoci coincident at the center, and the directrices infinitelydistant. 117. The sum of the focal distances of any point on an ellipse isconstant; it… … Fia. 81. then FiPi = e(ZO + OM) = e(-+x\ = a 4- esB,. 196 SPECIAL PROPERTIES OF THE CONICS [Ch. IX Also F^Pt, = e{OZ- OM) = a — ej\.Hence, by addition, F^P^ + F^Pi = 2 a; i.e., the sum of the focal distances of any point on an ellipseis constant; it is equal to the major axis. This property gives…
Geometry, Analytic
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