CO-Tf1 Conical Polar

The polar of some point P wrt some conic CO is the line L connecting the points of tangency of the tangents through P at CO.

In this construction P is called the pole and L is called the polar.

This construction is very intuitive. However there is a flaw in the definition because the polar cannot be constructed under all circumstances. For example when CO is some ellipse and P is drawn within the ellipse, then the construction fails.

Therefore another construction is made that includes the result of the first construction:

The polar of some point P wrt some conic is the 3rd diagonal (see QG-L1 in EQF) of any quadrigon formed by the intersection points of any 2 lines through P with the conic.

Properties

• The polar line of the focus of a parabola is the directrix

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