Ellipse properties
Definitions shown in Ellipse
Ellipse and tangent
Let an ellipse with foci
and the point
outside
be given.
Let
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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