Chapter 8.3, Problem 3E

To determine

To fill the blanks:

The standard equation of an ellipse with centre $(0,0)$ , vertices $\left(\pm a,0\right)$ and foci $\left(\pm c,0\right)$ is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , where $b^2=$ ---------------------.