1. The problem: Find the equation of an ellipse given its vertices. 2. Recall the standard form of the ellipse equation centered at the origin with horizontal major axis: $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $$ where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. 3. The vertices are located at $(\pm a,0)$ if the major axis is horizontal, or at $(0,\pm a)$ if vertical. 4. Given the vertices, identify $a$ as the distance from the center to a vertex. 5. Next, determine $b$: If the co-vertices or minor axis length is known, use $b$ accordingly. If not given, $b$ cannot be determined uniquely. 6. Write the ellipse equation with the identified $a$ and $b$ values. Example: If vertices are at $(\pm 5,0)$ and minor axis length $6$, then $a=5$ and $b=3$. Equation: $$ \frac{x^2}{5^2} + \frac{y^2}{3^2} = 1 $$ Final answer: $$\frac{x^2}{25} + \frac{y^2}{9} = 1$$