# 11. Find the equation for the ellipse that satisfies the given conditions:       Vertices (0, ± 13), foci (0, ± 5)

Given, In an ellipse,

Vertices (0, ± 13), foci (0, ± 5)

Here Vertices and focus of the ellipse are in Y-axis so the major axis of this ellipse will be Y-axis.

Therefore, the equation of the ellipse will be of the form:

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

Where $a$ and $b$are the length of the semimajor axis and semiminor axis respectively.

So on comparing standard parameters( vertices and foci) with the given one, we get

$a=13$ and $c=5$

Now, As we know the relation,

$a^2=b^2+c^2$

$b^2=a^2-c^2$

$b=\sqrt{a^2-c^2}$

$b=\sqrt{13^2-5^2}$

$b=\sqrt{169-25}$

$b=\sqrt{144}$

$b=12$

Hence, The Equation of the ellipse will be :

$\frac{x^2}{12^2}+\frac{y^2}{13^3}=1$

Which is

$\frac{x^2}{144}+\frac{y^2}{169}=1$.

Exams
Articles
Questions