Ellipse properties
Definitions shown in Ellipse
Ellipse and tangent
Let an ellipse with foci
and the point
outside
be given.
Let centered at
be the circumcircle of given ellipse.
Let be the inverse of a point
with respect to
Let be the point of the ellipse such that
Prove that is tangent to the ellipse.
Proof
Let equation of the ellipse be
The radus of the circumcircle is
so
Denote so the point
The slope of the tangent at point
is:
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