The ellipse is the stretch of a circle.
First of all inverse stretch the given ellipse into the circle.
This inverse stretch transforms point P into P'.
The searched ellipse is the direct transform of an ellipse containing the circle and P'.
This ellipse containing the circle and P' needs to have a curvature radius in A ≥ circle radius.
As the major axis is AP' = 2a, the curvature radius at vertex A being b²/a,
we get b = O'B from b² = R.a by a classical construction.
This gives the cyan ellipse.
Then the direct stretch transforms this ellipse into the searched one in red.
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