Question:
Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(\pm 3,0)$, ends of minor axis $(0, \pm 2)$
Solution:
Ends of major axis $(\pm 3,0)$, ends of minor axis $(0, \pm 2)$
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 $\frac{x^{2}}{3^{2}}+\frac{y^{2}}{2^{2}}=1$ i.e., $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$.