Questions: What are the vertices of the ellipse defined by the equation x^2/4 + y^2/25 = 1? (2,0) and (-2,0) (4,0) and (-4,0) (0,5) and (0,-5) (0,25) and (0,-25) (2,5) and (4,25)

Solution Steps

The given equation of the ellipse is:

\[ \frac{x^2}{4} + \frac{y^2}{25} = 1 \]

This is in the standard form of an ellipse:

\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]

where \(a^2 = 4\) and \(b^2 = 25\).

Since \(b^2 > a^2\), the major axis of the ellipse is along the \(y\)-axis.

For an ellipse centered at the origin with a vertical major axis, the vertices are located at \((0, \pm b)\).

Given \(b^2 = 25\), we find \(b = \sqrt{25} = 5\).

Thus, the vertices are at \((0, 5)\) and \((0, -5)\).

Final Answer