Parabola given by two points and their tangents
A parabola is given by two points and the tangents passing through them. construct additional points with tangents.
1. Points P and Q are given, as well as tangents tangents tP and tQ.
2. Connect P to Q.
3. Find the midpoint (construction not depicted).
4. Connect the midpoint to the intersection point of the tangents. This line is parallel to the axis of the parabola.
5. The midpoint of this segment is point R, a point of the parabola.
6. The tangent is parallel to segment PQ.
7-16. Repeat the previous construction with the help of the new point and tangent. Note: the yellow lines are all parallel to each other and the axis of the parabola (the axis is not constructed.
17. Repeat the process as much as necessary to get an accurate curve.
18. The axis of the parabola without the depiction of its construction just to show its parallelism to the yellow lines.