Ellipse bounding a rectangle [closed]

Answer 1

1. Ellipse formula is (x/A)^2+(y/B)^2=1, where A and B are radiuses of ellipse
2. Rectangle sides are Rw and Rh
3. Let's assume we want ellipse with same proportions as rectangle; then, if we image square in circle (A=B,Rq=Rh) and squeeze it, we well keep ratio of ellipse A/B same as ratio of rectangle sides Rw/Rh;

This leads us to following system of equations:
(x/A)^2+(y/B)^2=1
A/B=Rw/Rh

Lets solve it: A=B*(Rw/Rh)
(Rh/2B)^2+(Rh/2B)^2=1
Rh=sqrt(2)*B

And final solution:
A=Rw/sqrt(2)
B=Rh/sqrt(2)

Example: