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Ellipse, simple!
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Translate the rectangle to (0,0). Then the four corners are (e,f), (-e,f), (-e,-f), (e,-f). These points should be on the ellipse. The equation of the ellipse (at the origin, if its longest radius lies on a coordinate axis) is generally
b^2*x^2 + a^2*y^2 = a^2*b^2
where a and b are the longest and the shortest radiuses of the ellipse. Now you can substitute x with e and y with f. Then fix a value for a or b and calculate the other value (a or b) from the equation and you''ll get your ellipse equation with putting these a and b values into the general ellipse equation. Because you must fix one of the values a and b, there is an infinite
b^2*x^2 + a^2*y^2 = a^2*b^2
where a and b are the longest and the shortest radiuses of the ellipse. Now you can substitute x with e and y with f. Then fix a value for a or b and calculate the other value (a or b) from the equation and you''ll get your ellipse equation with putting these a and b values into the general ellipse equation. Because you must fix one of the values a and b, there is an infinite
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