I have an ellipse with a long aspect of a and a short aspect of b. The equation for this ellipse is found on this post: What is the general equation of the ellipse that is not in the origin and rotated by an angle?. My ellipse is contained in a circle of radius b. If the ellipse could be randomly oriented by angle A within the sphere, what is the probability density function of being in the ellipse as a function of the distance away from the sphere's center? Effectively, I'm looking for the density function that results from rotating an ellipse from [0,2 Pi). Is this as simple as integrating the equation for the ellipse over the angle, A?
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