Hyperbola
Orthogonal tangents – orthoptic

For a hyperbola x 2 a 2 − y 2 b 2 = 1, a > b {\textstyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1,\,a>b} 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 the orthoptic of the given hyperbola.

The tangents may belong to points on different branches of the hyperbola.

In case of a ≤ b {\displaystyle a\leq b} there are no pairs of orthogonal tangents.
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