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

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

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

$\frac{x^2}{2}+\frac{y^2}{5}=1$

$\frac{x^2}{5}+\frac{y^2}{2}=1$

Verified step by step guidance

Identify the center of the ellipse. Since the ellipse is centered at the origin, the center is at (0,0).

Determine the lengths of the semi-major and semi-minor axes by looking at the intercepts on the x- and y-axes. 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.

Recall the standard form equation of an ellipse centered at the origin: $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, where $a$ is the length of the semi-major axis and $b$ is the length of the semi-minor axis.

Substitute the values of $a$ and $b$ into the equation: $a = 5$ and $b = 2$, so the equation becomes $\frac{x^2}{2^2} + \frac{y^2}{5^2} = 1$.

Simplify the denominators to get the final standard form: $\frac{x^2}{4} + \frac{y^2}{25} = 1$.

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