11. Find the equation for the ellipse that satisfies the given conditions:

       Vertices (0, ± 13), foci (0, ± 5)

Answers (1)

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 bare 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.

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