Ellipse
Orthogonal tangents

For the ellipse x 2 a 2 + y 2 b 2 = 1 {\displaystyle {\tfrac {x^{2}}{a^{2}}}+{\tfrac {y^{2}}{b^{2}}}=1} the intersection points of orthogonal tangents lie on the circle x 2 + y 2 = a 2 + b 2 {\displaystyle x^{2}+y^{2}=a^{2}+b^{2}}.

This circle is called orthoptic or director circle of the ellipse (not to be confused with the circular directrix defined above).
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