Orthoptic curve (director circle) of a hyperbola

Check existence and nature of the orthoptic of a hyperbola

1. A hyperbola has not always an orthoptic curve: its existence depends on the eccentricity of the hyperbola, i.e. on the angle between the asymptotes. 2. If the given hyperbola has an orthoptic curve, this curve is also called the director circle of the hyperbola. 3. Here the hyperbola (in blue) is given by a canonical equation. Check the existence of the director circle (in red) when changing the values of the parameters.