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.
