Definition:Eccentric Circle of Central Conic

Definition

Let $\KK$ be a central conic whose center is at $O$.

The eccentric circles of $\KK$ are the two circles whose center is at $O$ and whose diameter coincides with either the major axis of $\KK$ or the minor axis of $\KK$.

Eccentric Circle of Ellipse

Let $\KK$ be an ellipse whose center is at $O$.

The eccentric circles of $\KK$ are the two circles whose center is at $O$ and whose diameter coincides with either the major axis of $\KK$ or the minor axis of $\KK$.

Eccentric Circle of Hyperbola

Let $\KK$ be a hyperbola whose center is at $O$.

The eccentric circles of $\KK$ are the two circles whose center is at $O$ and whose diameter coincides with either the major axis of $\KK$ or the minor axis of $\KK$.

Also see

• Definition:Eccentric Circles, a completely different concept

• Results about eccentric circles of central conics can be found here.

Sources

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