Question #3e00c

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Answer 1 · 2016-09-15T09:38:00

see 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 $A_E=2A_C$

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

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

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

$=> r=50% b$