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## Main Question or Discussion Point

I have a circle defined by the intersection of a sphere and a plane.* I want to convert from cartesian to parametric form on my way to finding the closest point on the circle to some arbitrary other point.* How do I go about this?* Alternatively, how do I find the closest point?

The equation of the sphere is x^2 + y^2 + z^2 = R^2.

The equation of the plane is:* xsub0*x + ysub0*y + zsub0*z = R^2 - r^2/2 where (xsub0,ysub0,zsub0) happens to be another point in space.

I want to find the closest point on the circle to (xsub1,ysub1,zsub1).

The equation of the sphere is x^2 + y^2 + z^2 = R^2.

The equation of the plane is:* xsub0*x + ysub0*y + zsub0*z = R^2 - r^2/2 where (xsub0,ysub0,zsub0) happens to be another point in space.

I want to find the closest point on the circle to (xsub1,ysub1,zsub1).