Answer
\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\text{ where }{{a}^{2}}={{b}^{2}}+{{c}^{2}}\]
Work Step by Step
\[\begin{align}
& \text{The equation of the standard ellipse with vertices at }\left( \pm a,0 \right) \\
& \text{and foci at }\left( \pm c,0 \right)\text{ is:} \\
& \frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\text{ where }{{a}^{2}}={{b}^{2}}+{{c}^{2}} \\
\end{align}\]
