Oh, I didn't see that you needed a set number of points.
Well, the number of points inside is going to be roughly:
n_points = (pi/4) * (2*radii.y)/y_dis * (2*radii.x)/min_dis
Substitute min_dis * sqrt(0.75) in for y_dis and solve for min_dis.
That's just an estimate, so you could just use that and cheat a little by keeping a count and stopping once you've reach the amount. I'll have to think more about how you would do it more precisely.