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Collisions of 2 ellipse and their direction of motion after collision

i am doing a project which requires collision of two ellipse. I am using ellipse in canvas. i am new to games that is why i need help. I know how to move ellipse in canvas and collision with boundaries but collision of two ellipse is a tricky part. I cannot get the perfect logic out of it. What should i do? Or what methods, properties or formulas i should use to improvise? Suggestions required

another thing is that if the collision has taken place at some point, how would it be possible to give new directions to both ellipse? 


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