The points A = (−1,1) and B = (1,1) lie on the parabola [math]y = x^2[/math]. Among all points
P = (x,y) on the parabola [math]y = x^2[/math] with y ≤ 1, determine the points that
(a) maximize[math] |P A|^2 + |P B|^2[/math], (b) minimize[math] |P A|^2 + |P B|^2[/math]
