Does any ellipse $E$ have a circle $C$ such that you can obtain $E$ by transforming $C$ by a simple formula $F$? In details , both $E$ and $C$ have the same center and the axes of $E$ are the XY axes. And F moves $(x,y)$ to $( m*x , y)$ . Where m is a real number.
Thank you in advance.
I think you'll see it from $$ {\rm ellipse:\ \ }{x^2\over a^2}+{y^2\over b^2}=1. $$
$$ {\rm circle:\ \ } {x^2\over b^2}+{y^2\over b^2}=1. $$