Parabola 1Given the axis, the axial vertex (V), and one tangent line, construct the parabola and the point of tangency.  Let the tangent line and the axis meet at point A. Construct B so that V is the midpoint of AB. A line through B and perpendicular to the axis meets the line of tangency at C. This is the point of tangency. Construct the diameter through C parallel to the axis. Reflect this diameter across the tangent line. The reflection image meets the axis at F, the focus. Reflect the focus across that same tangent line. Its image, Fʹ, falls on the directrix. Construct it perpendicular to the axis.  We now have the focus and directrix. The parabola may be constructed from those objects alone. The WebSketchpad image below is interactive. Drag the given objects to see changes in the construction. |