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?

Answer 1

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:

$\boxed{\frac{x^2}{25} + \frac{y^2}{9} = 1}$.