Given the width and height of an ellipse find n number of points around the ellipse?

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I am looking to find $n$ number of points around an ellipse. They don't necessarily have to be equidistant.

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You can take the points $P_k=(x_k,y_k)$, with $$ x_k=a\cos(2k\pi/n)\\ y_k=b\sin(2k\pi/n) $$ for $k=0,\ldots,n-1$, and where $a,b$ are the semi-wight and the semi-heigth, respectively.