# 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 y^{2}/a^{2} - x^{2}/b^{2} = 1

Since the vertices are (0, ± 5), a = 5

Since the foci are (0, ± 8), c = 8

We know that, c^{2} = a^{2} + b^{2}

Hence,

⇒ 5^{2} + b^{2} = 8^{2}

⇒ b^{2} = 64 - 25

⇒ b^{2} = 39

Thus, the equation of the hyperbola is y^{2}/25 - x^{2}/39 = 1

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 y^{2}/25 - x^{2}/39 = 1 while the Vertices are (0, ± 5) and Foci are (0, ± 8)

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