Category:Definitions/Eccentric Angles
This category contains definitions related to Eccentric Angles.
Related results can be found in Category:Eccentric Angles.
Let $\KK$ be a central conic.
Let $P$ be a point on $\KK$.
Let $\CC$ be the auxiliary circle of $\KK$.
The eccentric angle of $P$ with respect to $\KK$ is defined as follows:
Ellipse
Let $\KK$ be an ellipse 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 produced so as to meet $\CC$ at $P'$.
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 $\KK$.
Hyperbola
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 $\KK$.
Pages in category "Definitions/Eccentric Angles"
The following 5 pages are in this category, out of 5 total.