1. The problem is to find the eccentricity $e$ of a conic section. 2. The eccentricity $e$ is defined as the ratio of the distance from any point on the conic to the focus, divided by the perpendicular distance from that point to the nearest directrix. 3. For ellipses and hyperbolas, the eccentricity is given by the formula: $$e = \frac{c}{a}$$ where $c$ is the distance from the center to a focus, and $a$ is the distance from the center to a vertex along the major axis. 4. Important rules: - For ellipses, $0 < e < 1$. - For hyperbolas, $e > 1$. - For parabolas, $e = 1$. 5. To find $e$, you need the values of $c$ and $a$ from the conic's equation or geometric properties. 6. Once $c$ and $a$ are known, substitute into the formula and simplify. 7. Example: If $c = 5$ and $a = 13$, then $$e = \frac{5}{13}$$ 8. This fraction cannot be simplified further, so the eccentricity is $\frac{5}{13}$. This completes the calculation of eccentricity for the given conic section.