Parabola 8Given the focus (F) and two points (P1 and P2) on the curve, construct a parabola.  On each of the points P1 and P2 center a circle passing through the focus. Any external common tangent to both circles can serve as a directrix. Construct line P1P2. Through P1 and P2 construct perpendiculars to this line. Let them intersect the respective circles at points A and B, on the same side of P1P2. Let AB meet P1P2 at point H. This is a center of homothety of the circles.  Construct the circle with diameter HP1. Let it intersect circle P1 at C and D. Lines HC and HD are external common tangents of circles P1 and P2, and are directrices for the solution parabolas.  Now having the focus and directrix, the parabola, axis, and axial vertex can be constructed for each of the two solutions. |