Definition:Auxiliary Circle

Definition

Let $\KK$ be a central conic, that is, an ellipse or a hyperbola.

The auxiliary circle of $\KK$ is the eccentric circle whose diameter coincides with the major axis of $\KK$.

Auxiliary Circle of Ellipse

Let $E$ be an ellipse.

The auxiliary circle of $E$ is the eccentric circle whose diameter coincides with the major axis of $E$:

In the above diagram, the auxiliary circle of $E$ is the circle $C$.

Auxiliary Circle of Hyperbola

Let $H$ be a hyperbola.

The auxiliary circle of $H$ is the eccentric circle whose diameter coincides with the major axis of $H$:

In the above diagram, the auxiliary circle of $H$ is the circle $C$.

Also see

• Results about auxiliary circles can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): auxiliary circle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): auxiliary circle