1) Find the intersection point E of the normal at A with the polar p of A w.r. to the circle (c).

2) Take the symmetric A* of E with respect to A. This is the required center of curvature at the point A, the radius being equal to R = |A*A|, the curvature of (e) at being k = 1/R.

An easy calculation for the curvature point A*(x*,y*) in terms of A(x,y) gives the following equation:

The figure above shows the circle (f) passing through A and F, which is the inverse of A w.r. to (c), hence orthogonal to it. It shows also the locus of A* [Ellipse Evolute], which is the envelope of the normals of the ellipse.

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