Write the standard form equation of each ellipse centered at the origin.

• A. $\frac{x^2}{4}+\frac{y^2}{25}=1$
• B. $\frac{x^2}{25}+\frac{y^2}{4}=1$
• C. $\frac{x^2}{2}+\frac{y^2}{5}=1$
• D. $\frac{x^2}{5}+\frac{y^2}{2}=1$

Answer: (A)

Verified step by step guidance

1. Identify the center of the ellipse. Since the ellipse is centered at the origin, the center is at (0, 0).
2. Determine the lengths of the semi-major and semi-minor axes by looking at the intercepts on the x-axis and y-axis. The ellipse extends from -2 to 2 on the x-axis, so the semi-minor axis length is 2. It extends from -5 to 5 on the y-axis, so the semi-major axis length is 5.
3. Recall the standard form equation of an ellipse centered at the origin: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where \(a\) is the length of the semi-major axis and \(b\) is the length of the semi-minor axis. Since the major axis is vertical, \(a\) corresponds to the y-axis and \(b\) corresponds to the x-axis.
4. Substitute the values of \(a\) and \(b\) into the equation: \(a = 5\) and \(b = 2\), so the equation becomes \(\frac{x^2}{2^2} + \frac{y^2}{5^2} = 1\).
5. Simplify the denominators to get the final standard form equation: \(\frac{x^2}{4} + \frac{y^2}{25} = 1\).