Finding area of elliptical ring (phase space) (1 Viewer)

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To make a long story short, the problem has an elliptical ring from width E to E+dE in phase space (p on y axis, x on x axis). This is a harmonic oscillator, so the standard equations apply (E=p^2/2m + kx^2/2)... now for the question I need to find the total area in the ring of the ellipse in a slice from x to x + dx and divide it by the total area of the ring, but I don't know how to do that. I know the total area of the ring (should be just dE), but I can't seem to find out how to get the area of a narrow slice of this thing without complex integration (which I don't believe is necessary for this). Anyone have any ideas to push me in the right direction?
 

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