# Find the equation of the hyperbola satisfying the given conditions: Foci (± 5, 0), the transverse axis is of length 8

**Solution:**

Foci (± 5, 0), the transverse axis is of length 8.

Here,

the foci are on the x-axis.

Therefore,

the equation of the hyperbola is of the form x^{2}/a^{2} - y^{2}/b^{2} = 1

Since the foci are (± 5, 0), c = 5

Since the length of the transverse axis is 8,

Then,

⇒ 2a = 8

⇒ a = 4

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

Hence,

⇒ 4^{2} + b^{2} = 5^{2}

⇒ b^{2} = 25 -16

⇒ b^{2} = 9

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

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 10

## Find the equation of the hyperbola satisfying the given conditions: Foci (± 5, 0), the transverse axis is of length 8.

**Summary:**

The equation of the hyperbola is x^{2}/16 - y^{2}/9 = 1 while the Foci are (± 5, 0), and the transverse axis is of length 8

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