A Theorem of Steiner's

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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 ľa.


Name Input
Orthocenter Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image