Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 324
AND POLARS 305 y.Y,y line, the axis of x, goes over into a parallel line-segment, AA,of equal length, and the mid-point, 0, of AA goes overinto the mid-point, 0, of AA. Let the circle be referred toaxes (x, y) with the origin at O,the axis of x lying along AA.Its equation will be (1) 2? + y^ = a\… … ■x Y=Vy, or x=X, - YV = — It follows, then, that the circle (1) is transformed into thecurve or(2) X^ + -f = a, X2 Y2 a2 &^ b = la. Thus the circle is seen to be carried into an ellipse. It remains to prove that the lines D and D, into which two conjugate diameters D and D of the circle are…
