Question

The parabola P: y=a-x^2, a>0, is cut by the line L: y=h, h>0, in the points A and B. the points C and D, on the x-axis, are such that ABCD is a rectangle, R.

(a)Find the coordinates for the vertices of R.
(b)Find the value(s) of h so that R has the greatest area.