#### Answer

(a=80 and b=20) or (a=20 and b=80)

#### Work Step by Step

Area of the circle = $\pi r^2=\pi (40)^2=1600\pi$
A = $\pi ab= \pi a(100-a)$ (area of the ellipse given a+b=100)
$1600 \pi = \pi a(100-a)$
1600 = a(100-a)
$a^2-100a+1600=0$
(a-80)(a-20)=0
a = 80 giving b=20 or
a=20 giving b=80