An ellipse has a vertex at (0, –5), a co-vertex at (–3, 0), and a center at the origin. Which is the equation of the ellipse in standard form?
The standard form equation for an ellipse centered at the origin is:
$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
where $a$ is the length from the center to a vertex, and $b$ is the length from the center to a co-vertex.
In this case, the vertex is at (0, -5), so $a = 5$. The co-vertex is at (-3, 0), so $b = 3$.
Thus, the equation of the ellipse in standard form is:
$\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1$
Simplifying, we have:
$\frac{x^2}{25} + \frac{y^2}{9} = 1$
So, the equation of the ellipse in standard form is:
$\boxed{\frac{x^2}{25} + \frac{y^2}{9} = 1}$.