Definition:Conjugate Lines

This page is about Conjugate Lines. For other uses, see Conjugate.

Definition

Let $\CC$ be a circle.

Let $\PP$ and $\QQ$ be the straight lines in the plane of $\CC$.

Let $P$ and $Q$ be the poles of $\PP$ and $\QQ$ with respect to $\CC$ respectively.

Let $P$ and $Q$ be such that $P$ lies on $\QQ$ and $Q$ lies on $\PP$.

Then $\PP$ and $\QQ$ are known as conjugate lines with respect to $\CC$.

Also see

• Reciprocal Property of Pole and Polar

• Definition:Conjugate Points (Geometry)

• Results about conjugate lines can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $8$. Reciprocal property of pole and polar