Question

Find the equation for the ellipse that satisfies the given conditions: Length of major axis $26$, foci $(\pm 5,0).$

Answer 1

It is given that, length of major axis $26,$ foci $(\pm 5,0)$.
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.
$\Rightarrow 2a=26\Rightarrow a=13$ and $ae=5$
We know that, $b^2=a^2-a^2{e}^2=169-25=144$
Thus, the equation of the ellipse is $\frac{x^2}{169}+\frac{y^2}{144}=1$