Find the equation of the ellipse, whose length of the major axis is 20 and foci are $\left(0,\pm 5\right)$.

Solution: Equation of ellipse can be given as
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Here, Foci of ellipse $=\left(0\pm 5\right)$
This mean, the major axis is Y-axis and $c=5$.
Length of major axis $=20$
$\Rightarrow 2b=20\Rightarrow b=10$
$\therefore a^2=b^2-c^2=100-25=75$
So, the equation of the ellipse will be,$\frac{x^2}{75}+\frac{y^2}{100}=1$