Answer:
The eccentricity (\(e\)) of an ellipse is related to its foci and vertices by the equation:
\[ e = \frac{c}{a} \]
where:
- \(c\) is the distance from the center to each focus,
- \(a\) is the semi-major axis.
For the given ellipse, you're provided with the foci at (0, -5) and (0, 5). The distance between the center and each focus (\(c\)) is 5 units. Since the eccentricity (\(e\)) is given as \(1/4\), you can find the semi-major axis (\(a\)) using the formula:
\[ e = \frac{c}{a} \]
\[ \frac{1}{4} = \frac{5}{a} \]
Solving for \(a\):
\[ a = 20 \]
Now that you have the semi-major axis, you can find the vertices (\(a, 0\) and \(-a, 0\)) for the ellipse. In this case, the vertices are \((20, 0)\) and \((-20, 0)\).
