Parabola 5Given two tangent lines and the corresponding points (P1 and P2) of tangency, construct the parabola.  Let the tangent lines meet at A, and let M be the midpoint of P1P2. Line AM is a diameter of the parabola. Through P1 and P2 construct diameters parallel to AM. Reflect each of these diameters across its respective tangent line. These reflection images must meet at the focus, F. Reflect F across one of the tangent lines. Its image, Fʹ, falls on the directrix, which is constructed through Fʹ perpendicular to AM.  The solution parabola may now be constructed from the focus and directrix. |