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One method, called Acceptance/Rejectance or Thinning,
is to bound your ellipse by a box.
Generate random points within this box, then check if the points are within the ellipse. Throw away points that are not in the ellipse.
So the better you "bound" your shape, the less points you have to throw away.
In fact, since your ellipse is symmetrical about the x-axis, you can simply use 'half' and ellipse, the part thats above the x-axis.
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