Key Concepts

• Any conic may be determined by a single focus, the corresponding eccentricity, and the directrix. We can also define a conic in terms of a fixed point, the focus $P\left(r,\theta \right)$ at the pole, and a line, the directrix, which is perpendicular to the polar axis.
• A conic is the set of all points $e=\frac{PF}{PD}$, where eccentricity $e$ is a positive real number. Each conic may be written in terms of its polar equation.
• The polar equations of conics can be graphed.
• Conics can be defined in terms of a focus, a directrix, and eccentricity.
• We can use the identities $r=\sqrt{{x}^{2}+{y}^{2}},x=r\text{ }\cos \text{ }\theta$, and $y=r\text{ }\sin \text{ }\theta$ to convert the equation for a conic from polar to rectangular form.

Glossary

eccentricity

the ratio of the distances from a point $P$ on the graph to the focus $F$ and to the directrix $D$ represented by $e=\frac{PF}{PD}$, where $e$ is a positive real number

polar equation

an equation of a curve in polar coordinates $r$ and $\theta$