Projection of a circle to a plane in 3D

Can anyone suggest (with proof) how to derive the equation of a shape, when a circle is projected to a arbitrary plane in 3D?

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answer

Having given circle equation and the normal to the plane, you can get the equation of the projection cylinder.
Then all you have to do is to intersect this cylinder with the projection plane. For further detail please be more specific .

... However the suggested

... However the suggested solution will not calculate an orthogonal projection

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