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

Solution: Equation of ellipse can be given as
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Here, Foci of ellipse $=\left(\pm 5,0\right)$
So, $X$-axis is major axis and $c=5$
Length of major axis $=26$
$2a=26\Rightarrow a=13$
$\therefore b^2=c^2-a^2=169-25=144$
So, equation of required ellipse will be,
$\frac{x^2}{169}+\frac{y^2}{144}=1$