Definition:Eccentric Angle/Hyperbola

Definition

Let $\KK$ be a hyperbola with foci at $F_1$ and $F_2$.

Let $P$ be a point on $\KK$.

Let $\CC$ be the auxiliary circle of $\KK$ with center $O$.

Let $PQ$ be dropped perpendicular to the major axis $F_1 F_2$ of $\KK$ such that $Q$ lies on $F_1 F_2$.

Let $QP'$ be drawn tangent to $\CC$ such that $P'$ is the point of tangency with $\CC$.

The angle $QOP'$ is the eccentric angle of $P$ with respect to $\KK$.

In the above diagram, $\alpha$ is the eccentric angle of $P$ with respect to $\KK$.

Also see

• Results about eccentric angles can be found here.

Sources

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