Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $\left(\pm 3,0\right)$ ends of minor axis $\left(0,\pm 2\right).$ 

It is given that, ends of major axis $\left(\pm 3,0\right)$ and ends of minor axis $\left(0,\pm 2\right)$ 
Clearly, here the major axis is along the $x$-axis. 
Therefore, the equation of the ellipse will be of the form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, where $a$ is the semi-major axis.
Accordingly $a=3$ and $b=2$
Thus, the equation of the ellipse is $\frac{x^2}{3^2}+\frac{y^2}{2^2}=1i.e.,\frac{x^2}{9}+\frac{y^2}{4}=1$