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

**Solution:**

Vertices (0, ± 13), Foci (0, ± 5)

Here, the vertices are on the x-axis.

Therefore,

the equation of the ellipse will be of the form x^{2}/b^{2} + y^{2}/a^{2} = 1 where a is the semi major axis.

Accordingly, a = 13 and c = 5

It is known that a^{2} = b^{2} + c^{2}

Hence,

⇒ 13^{2} = b^{2} + 5^{2}

⇒ 169 = b^{2} + 25

⇒ b^{2} = 169 - 25

⇒ b^{2} = 144

⇒ b = 12

Thus, the equation of the ellipse is x^{2}/12^{2} + y^{2}/13^{2} = 1 or x^{2}/144 + y^{2}/169 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 11

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

**Summary:**

The equation of the ellipse is x^{2}/144 + y^{2}/169 = 1 while Vertices is (0, ± 13) and Foci is (0, ± 5)

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