Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ± 5), Foci (0, ± 8)

Solution:

Vertices (0, ± 5), Foci (0, ± 8)

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, ± 5), a = 5

Since the foci are (0, ± 8), c = 8

We know that, c² = a² + b²

Hence,

⇒ 5² + b² = 8²

⇒ b² = 64 - 25

⇒ b² = 39

Thus, the equation of the hyperbola is y²/25 - x²/39 = 1

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 8

Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ± 5), Foci (0, ± 8)

Summary:

The equation of the hyperbola is y²/25 - x²/39 = 1 while the Vertices are (0, ± 5) and Foci are (0, ± 8)