Find the area of an infinitesimal elliptical ring. I have an ellipse given by,
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=c$$
and another ellipse that is infinitesimally bigger than the previous ellipse, i.e.
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=c+dc$$
I want to find the area enclosed by the ring from $x$ to $x+dx$ but I don't know how. Please don't solve the question, just point me in the right direction, I want to solve it myself. Here is a picture of what I want to do.


Note that you just scaled up both the major and minor axes by a common factor $ \sqrt c$
You want to look at 
$$   (\sqrt c\, y )\ d (\sqrt c  x ) -  y\ dx = (c-1) y\ dx . $$ 
