The fixed point P(x, y) is on the curve x 2/4+y 2/b 2 = 1 (b > 0).

Let: x=2cosa, y=bsina.

x^2+2y

=4(cosa)^2+2bsina

=-4(sina)^2+bsina+4

=-4(sina-b/8)^2+4+b^2/ 16

When b/8≤ 1

When b/8 > 1, that is, point b>8, and the maximum value is b (Sina = 1 at this time).