Find the equation of the hyperbola satisfying the given conditions: Vertices (± 2, 0) , Foci (± 3, 0)

Solution:

Vertices (± 2, 0), Foci (± 3, 0)

Here, the vertices are on the ix-axis.

Therefore,

the equation of the hyperbola is of the form x²/a² - y²/b² = 1

Since the vertices are (± 2, 0), a = 2

Since the foci are (± 3, 0), c = 3

We know that, c² = a² + b²

Hence,

⇒ 2² + b² = 3²

⇒ b² = 9 - 4

⇒ b² = 5

Thus, the equation of the hyperbola is x²/4 - y²/5 = 1

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 7

Find the equation of the hyperbola satisfying the given conditions: Vertices (± 2, 0) , Foci (± 3, 0)

Summary:

The equation of the hyperbola is x²/4 - y²/5 = 1 while Vertices are (± 2, 0) and Foci are (± 3, 0)