CU-P-P1  Tangential of P

The tangential of a point P on CU is the intersection of the tangent at P with CU. Since any line always intersects a cubic at three points (real or imaginary), and a point of tangency counts twice, each point on CU will have exactly one tangential.

There is a simple construction:

1. Start with P and 2 random points P1,P2 on a cubic CU.
2. Draw line PP1 intersecting CU in S1.
3. Draw line PP2 intersecting CU in S2.
4. Draw line S1P2 intersecting CU in T2.
5. Draw line S2P1 intersecting CU in T1.

Let T be the 3rd intersection point of T1T2 with CU.

T is the Tangential of P (CU-P-P1) and PT will be the Tangent at P to CU.

See also QPG#2111.

CU-P-P1 P-Tangential-00.fig

Estimated human page views: 6