Ellipse

Smallest ellipse containing given ellipse and given point.

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.

Sorry, your browser is not Java compliant.

 

Home Arithmetic Geometric Misc Topics Scripts Games Exercices Mail Version Franšaise Previous topic Next topic