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

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

Given:

$Vertices\text{ }\left( 0,~\pm ~13 \right)\text{ }and\text{ }foci\text{ }\left( 0,~\pm \text{ }5 \right)$

Here, the vertices are on the

$x-pivot.$

Along these lines, the condition of the circle will be of the structure

${{x}^{2}}/{{b}^{2}}~+\text{ }{{y}^{2}}/{{a}^{2}}~=\text{ }1,~$

, where ‘a’ is the semi-significant pivot.

Then, at that point,

$a\text{ }=13\text{ }and\text{ }c\text{ }=\text{ }5.$

It is realized that

${{a}^{2}}~=\text{ }{{b}^{2~}}+\text{ }{{c}^{2}}.$

${{13}^{2}}~=\text{ }{{b}^{2}}+{{5}^{2}}$

$169\text{ }=\text{ }{{b}^{2}}~+\text{ }15$

${{b}^{2}}~=\text{ }169\text{ }\text{ }125$

$b\text{ }=~\surd 144$

$=\text{ }12$

∴ The condition of the circle is

${{x}^{2}}/{{12}^{2}}~+\text{ }{{y}^{2}}/{{13}^{2}}~=\text{ }1\text{ }or\text{ }{{x}^{2}}/144\text{ }+\text{ }{{y}^{2}}/169~=\text{ }1$

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