Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ± 3), Foci (0, ± 5)

Solution:

Vertices (0, ± 3), Foci (0, ± 5)

Here, the vertices are on the y-axis.

Therefore,

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

Since the vertices are (0, ± 3), a = 3

Since the foci are (0, ± 5), c = 5

We know that, c² = a² + b²

Hence,

⇒ 3² + b² = 5²

⇒ b² = 25 - 9

⇒ b² = 16

Thus, the equation of the hyperbola is y²/9 - x²/16 = 1

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 9

Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ± 3), Foci (0, ± 5)

Summary:

The equation of the hyperbola is y²/9 - x²/16 = 1 while the vertices are (0, ± 3) and the Foci are (0, ± 5)