Parabola 4Given the axis, the focus (F), and one point (P) on the curve, construct the parabolas. There generally are two solutions.  Through point P construct a diameter parallel to the axis. Construct the circle with center P and through focus F. Let the diameter intersect the circle at points A and B. Through A and B construct directrices perpendicular to the axis. Let the axis meet these directrices at C and D. Dilate these points with respect to F using scale factor 1/2. The images, Cʹ and Dʹ, are the axial vertices of the two parabolas.  The two solution parabolas may now be constructed from the directrices and their common focus. |