Find the equation of the ellipse which has Vertices (0, 13), foci… - Vidyadip

Question

Find the equation of the ellipse which has Vertices (0, $\pm$13), foci(0, $\pm$5)

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Answer

The foci $(0, \pm 5)$ lie on $y$-axis
So the equation of ellipse in standard form is $\frac{y^2}{a^2}+\frac{x^2}{b^2}=1$
Now vertices $(0, \pm a)$ is $(0, \pm 13)$
$\Rightarrow a=13$
Foci $(0, \pm \mathrm{c})$ is $(0, \pm 5)$
$\Rightarrow c=5$
We know that $c^2=a^2-b^2$
$\therefore(5)^2=(13)^2-b^2$
$\Rightarrow b^2=169-25=144$
Thus equation of required ellipse is
$\frac{x^2}{144}+\frac{y^2}{169}=1$

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