College Algebra, Chapter 8, 8.2, Section 8.2, Problem 10

Determine the vertices, foci and eccentricity of the ellipse $\displaystyle \frac{x^2}{16} + \frac{y^2}{25} = 1$. Determine the lengths of the major and minor
axes, and sketch the graph.
If we rewrite the given ellipse to $\displaystyle \frac{x^2}{4^2} + \frac{y^2}{5^2} = 1$, then it will have a form of
$\displaystyle \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$. So, the vertices of the ellipse is $(0,\pm a)$ which is $(0,\pm 5)$ and the foci of the ellipse
$c = \sqrt{a^2-b^2} = \sqrt{5^2 - 4^2} = 1$ is $(0,\pm 1)$. To determine the eccentricity of the ellipse we use the formula
$\displaystyle e = \frac{c}{a} = \frac{1}{5} = 0.20$. Next the lengths of the major and minor axes is determined to be $2a$ and $2b$ respectively.
So, the length of the major axis is $2(5) = 10$ while the length of the minor axis is $2(4) = 8$. Therefore, the graph is