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 x²/a² + y²/b² = 1 where a is the semi major axis.

Accordingly, a = 5 and c = 4

It is known that a² = b² + c²

Hence,

⇒ 5² = b² + 4²

⇒ 25 = b² + 16

⇒ b² = 25 - 16

⇒ b² = 9

⇒ b = 3

Thus, the equation of the ellipse is x²/5² + y²/3² = 1 or x²/25 + y²/9 = 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 x²/25 + y²/9 = 1 while Vertices is (± 5, 0) and Foci is (± 4, 0)