Matrix math for curved prims

Matrix math for curved prims
Is it possible to get a rotation matrix for a circular primitive, given a simple (I guess quadratic) Bézier curve?

All of our curved prims are circles or conical, and I’ve read that any affine transformation of a conic section will result in another conic section. If the simple Bézier curves are likewise conic (which may be a wrong assumption), then theoretically they can all be represented by a 2D shear matrix, right?
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