College Algebra, Chapter 8, 8.2, Section 8.2, Problem 16

Determine the vertices, foci and eccentricity of the ellipse $5x^2 + 6y^2 = 30$. Determine the lengths of the major and minor
axes, and sketch the graph.
If we divide both sides by $16$, then we have
$\displaystyle \frac{x^2}{6} + \frac{y^2}{5} = 1$
We'll see that the function has the form $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Since, the denominator of $x^2$ is
larger, then the ellipse has a horizontal major axis. This gives $a^2 = 6$ and $b^2 = 5$, so $c^2 = a^2 - b^2 = 6 - 5 = 1$. Thus, $a = \sqrt{6}$, $b = \sqrt{5}$
and $c = 1$. Then the following is determined as.

$
\begin{equation}
\begin{aligned}
\text{Vertices}& &(\pm a, 0) &\rightarrow (\pm \sqrt{6}, 0)\\
\\
\text{Foci}& &(\pm c, 0) &\rightarrow (\pm1, 0)\\
\\
\text{Eccentricity (e)}& &\frac{c}{a} &\rightarrow \frac{1}{\sqrt{6}}\\
\\
\text{Length of major axis}& &2a &\rightarrow 2 \sqrt{6}\\
\\
\text{Length of minor axis}& &2b &\rightarrow 2\sqrt{5}
\end{aligned}
\end{equation}
$