I have an ellipse with eccentricity $e_c$, semi-major axis and one focus is at $(0,0)$. Here is my graph.
So I am wondering, what is the equation of an ellipse in form $a(x+b)^2+y^2=r^2?$
Note: $b$ does not have to be a monomial or a constant. It can be of form $a+bx$ or $c(d+e)^f$, etc.