# Find the equation for the ellipse that satisfies the given conditions: Vertices (± 6, 0), Foci (± 4, 0)

**Solution:**

Vertices (± 6, 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 = 6 and c = 4

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

Hence,

⇒ 6^{2} = b^{2} + 4^{2}

⇒ 36 = b^{2} + 16

⇒ b^{2} = 36 - 16

⇒ b^{2} = 20

⇒ b = √20

Thus, the equation of the ellipse is x^{2}/6^{2} + y^{2 }/ (√20)^{2 }= 1 or x^{2}/36 + y^{2}/20 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 12

## Find the equation for the ellipse that satisfies the given conditions: Vertices (± 6, 0), Foci (± 4, 0)

**Summary:**

The equation of the ellipse is x^{2}/36 + y^{2}/20 = 1 While Vertices are (± 6, 0) and Foci are (± 4, 0)

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