Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 294
the parabola, 2/^ = 2 mx, meets the hyperbola, xy = c% in the points Pj and Pg.What is the locus of the mid-point, P, of P1P2 ? As auxiliary variables wetake the coordinates {x, y) ofthe point R tracing the parab-YiQ, 7 ola; they satisfy the equa- tion of the parabola: (4) ?/2 = 2 mx. The tangent… … x 276 ANALYTIC GEOMETRY Half the sum of the roots of this equation is X; hence, by (1), (6) X=-2 Since Y is the ordinate of the point on the line (5) whoseabscissa is given by (6), we have ^ x , A mx , (7) yY=m{-- + x We now have three equations, (4), (6), and (7), from whichto eliminate the…
