Question

Find the equation for the ellipse that satisfies the given conditions: Foci $(\pm 3,0),a=4.$

Answer 1

It is given that, foci $(\pm 3,0),a=4$
Since the foci are on the $x$-axis 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 $ae=3$ and $a=4$
We know that $a^2=b^2+a^2{e}^2$
$\therefore 4^2=b^2+3^2$
$\Rightarrow 16=b^2+9$
$\Rightarrow$ $b^2=16-9=7$
Thus, the equation of the ellipse is $\frac{x^2}{16}+\frac{y^2}{7}=1$