# The Isogonal Conjugate of a Line

- Author:
- Steve Phelps

- Topic:
- Geometry

The isogonal conjugate of a line is a circumconic through the vertices of the triangle.
If the line intersects the circumcircle in 2 real points, the circumconic is a hyperbola.
If the line intersects the circumcircle in 1 real points, the circumconic is a parabola.
If the line intersects the circumcircle in no real points, the circumconic is an ellipse.
Drag point X and Y to move the line. Drag point P or press the "play" button to animate point P.

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