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 x²/a² - y²/b² = 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, c² = a² + b²

Hence,

⇒ 4² + b² = 5²

⇒ b² = 25 -16

⇒ b² = 9

Thus, the equation of the hyperbola is x²/16 - y²/9 = 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 x²/16 - y²/9 = 1 while the Foci are (± 5, 0), and the transverse axis is of length 8