Answer
$\frac{x^2}{4}+\frac{y^2}{25}=1$
Work Step by Step
Step 1. Identify the given quantities: ellipse center $C(0,0)$, x-intercepts $\pm2$, y-intercepts $\pm5$
Step 2. As the center is at the origin, the intercepts can be used to calculate the axis length, we have $2a=5+5=10$ or $a=5$ along y-axis, and $2b=2+2=4$ or $b=2$ along x-axis.
Step 3. Write the equation for the ellipse as $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$, and we get the answer as
$\frac{x^2}{4}+\frac{y^2}{25}=1$
