The orthocenter of the triangle formed by three tangents to a parabola lies on the directrix. We create the parabola with vertex at the origin and focus at the point (0,a). The directrix is the line Y = -a. We see from the diagram that the y coordinate of the orthocenter is indeed –a.
Expressions
| Name | Input | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Orthocenter |  |
 |
 |
 |
 |
 |
 |
 |
 |
