10.4 The Ellipse

Since denominator of $x^2$ is larger, major axis is along x-axis. $a^2 = 25 \implies a = 5$. $b^2 = 9 \implies b = 3$.

1. c relationship: $c^2 = a^2 - b^2 = 25 - 9 = 16 \implies c = 4$.
2. Foci: $(\pm c, 0) = (\pm 4, 0)$.
3. Vertices: $(\pm a, 0) = (\pm 5, 0)$.
4. Major Axis: $2a = 10$.
5. Minor Axis: $2b = 6$.
6. Eccentricity: $e = c/a = 4/5$.
7. Latus Rectum: $2b^2/a = 2(9)/5 = 18/5$.