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

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

Since the foci are (0, ± 5), c = 5

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

Hence,

⇒ 3^{2} + b^{2} = 5^{2}

⇒ b^{2} = 25 - 9

⇒ b^{2} = 16

Thus, the equation of the hyperbola is y^{2}/9 - x^{2}/16 = 1

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 y^{2}/9 - x^{2}/16 = 1 while the vertices are (0, ± 3) and the Foci are (0, ± 5)