Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 100
res of its distances from twofixed points Pi, Po is constant,and equal to c: PPi - PP22 = c, (3) [PP2--PPi- = C. Take the mid-point of thesegment P1P2 as origin andthe axis of x along P1P2.The coordinates of Pi and Pgcan be Avritten as (—a, 0), (a, 0) ; those of P, as (x, y). By Ch. I, § 3, PP,2 =… … Fig. 2 82 ANALYTIC GEOMETRY {x + a)2+ y^-(x- ay - y^ = c,{x - ay+ If -{x + af - if = c. These reduce to (4) 4 aa; = c, 4 aa; = — c. Hence, if condition (3) is satisfied, P lies on one or theother of the lines Conversely, if P lies on one or the other of the lines (5),then (4) holds, and from (4) we…
