1. **Problem Statement:** Find the eccentricity and name of the conic given by the polar equation $$r = \frac{4}{4 - 2 \cos \theta}$$. 2. **Recall the standard form of a conic in polar coordinates:** $$r = \frac{ed}{1 + e \cos \theta}$$ or $$r = \frac{ed}{1 - e \cos \theta}$$ where $e$ is the eccentricity and $d$ is the distance from the pole to the directrix. 3. **Rewrite the given equation:** Given $$r = \frac{4}{4 - 2 \cos \theta}$$, divide numerator and denominator by 4: $$r = \frac{4}{4(1 - \frac{1}{2} \cos \theta)} = \frac{1}{1 - \frac{1}{2} \cos \theta}$$. 4. **Compare with standard form:** Here, $$e = \frac{1}{2} = 0.5$$ and $$d = 1$$. 5. **Interpretation:** Since $e = 0.5 < 1$, the conic is an ellipse. **Final answers:** - Eccentricity: $e = 0.5$ - Name of conic: Ellipse