Calculating a point on an ellipse

Let's say that I have two points A and B located around the circumference of an ellipse, and they form an angle X from the center point. Now let's say that point A moves to a new point C. How can I calculate a new point for B so that the angle X remains constant? Pointers to some code will be appreciated.

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Why not use the polar shape of the ellipse, where the angle is measured from the center of the ellipse? http://en.wikipedia.org/wiki/Ellipse#Polar_form_relative_to_center From this equation, if you know the value of the angle between A and B (say, theta), and you know the value of the central angle of the new point C (say, phi), then your the desired point D can be calculated from this polar form using the angle (theta + phi)

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