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# Find the equation for the ellipse that satisfies the given conditions: Vertices (± 5, 0), Foci (± 4, 0)

**Solution:**

Vertices (± 5, 0), Foci (± 4, 0)

Here, the vertices are on the x-axis.

Therefore,

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

Accordingly, a = 5 and c = 4

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

Hence,

⇒ 5^{2} = b^{2} + 4^{2}

⇒ 25 = b^{2} + 16

⇒ b^{2} = 25 - 16

⇒ b^{2} = 9

⇒ b = 3

Thus, the equation of the ellipse is x^{2}/5^{2} + y^{2}/3^{2} = 1 or x^{2}/25 + y^{2}/9 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 10

## Find the equation for the ellipse that satisfies the given conditions: Vertices (± 5, 0), Foci (± 4, 0)

**Summary:**

The equation of the ellipse is x^{2}/25 + y^{2}/9 = 1 while Vertices is (± 5, 0) and Foci is (± 4, 0)

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