CU-P-4P1

CU-P-4P1 Set of 4 tangency points from P to CU

On a general cubic CU we have 4 points of tangency of tangents from some point P to the cubic. They are the intersection points of CU and the P-Polar Conic (CU-P-Co1).

Infovisual CU-P-4P1-infovisual-cvt-01.png

CU-P-4P1 P-points of tangency-01.fig

There is an extra property for the Diagonal Triangle of the Quadrangle QA formed by the touchpoints of the tangents from some point P on CU. The vertices of its Diagonal Triangle also lie on CU and share the same tangential P’ with P, which is QA-Tf2(P).

Infovisual CU-P-4P1-infovisual-cvt-02.png

CU-P-4P1 P-points of tangency-02-plus DT.fig

CU Point Validation

2X + P = N has 4 solutions

Properties

When P = IP (Infinity Point of CU), then CU-P-4P1 = CU-IP-4P1.
The 4 points CU-P-4P1 form a Quadrangle QA. The Diagonal Triangle QA-DT of QA also has its vertices on CU.
For each such QA exists an Involutary Conjugate (CU-P-Tf1) mapping any point on CU to another point on CU.

Estimated human page views: 5