Question

Question #3e00c

Answer 1

see explanation.

Explanation:

Let a = major diameter of the ellipse,
let b = minor diameter of the ellipse,
let r= radius of the circle.

Area of the ellipse `(A_E) = pi(a/2)(b/2) = (piab)/4`

Area of the circle `(A_C) = pir^2`

Given that `a=2b`

`=> pi(ab)/4 =pi(2b^2)/4=1/2pib^2`

Given that `A_E=2A_C`

`=> 1/2pib^2 =2pir^2`

`r^2=1/4b^2`

`r=sqrt(1/4b^2) =1/2b`

`=> r=50% b`