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

Accordingly, a = 6 and c = 4

It is known that a² = b² + c²

Hence,

⇒ 6² = b² + 4²

⇒ 36 = b² + 16

⇒ b² = 36 - 16

⇒ b² = 20

⇒ b = √20

Thus, the equation of the ellipse is x²/6² + y² / (√20)² = 1 or x²/36 + y²/20 = 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 x²/36 + y²/20 = 1 While Vertices are (± 6, 0) and Foci are (± 4, 0)