Find constants so two ellipses enclose equal areas

by RoRi

May 31, 2016

Let $A, B$ be positive numbers with $A > B$ . Find values of $A$ and $B$ such that the area of the region enclosed by the ellipse

$Ax^2 + By^2 = 3$

is the same as the area bounded by the ellipse

$(A+B)x^2 + (A-B)y^2 = 3.$

Incomplete.

Stumbling Robot