Diameters of a parabola, after Apollonius

Check the boxes to see an equation for the curve in a coordinate system determined by the tangent at point D.
Move the point H to see that the equation is satisfied by all points on the parabola.
To change the shape of the parabola, move the focus, the directrix AB, or A and B individually. (Numbers in the equation will change to unpleasant decimals.)

Susan Addington, Created with GeoGebra

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