Find the equation of the hyperbola satisfying the given conditions: Foci (± 3√5, 0), the latus rectum is of length 8

Solution:

Foci (± 3√5, 0),

the latus rectum 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 (± 3√5, 0), c = ± 3√5

Since the length of latus rectum is 8,

Then,

⇒ 2b²/a = 24

⇒ b² = 4a

We know that, c² = a² + b²

Hence,

⇒ a² + 4a = 45

⇒ a² + 4a - 45 = 0

⇒ a² + 9a - 5a - 45 = 0

⇒ a (a + 9) - 5(a + 9) = 0

⇒ (a + 9)(a - 5) = 0

⇒ a = - 9, 5

Since a is non-negative, a = 5

Therefore,

⇒ b² = 4a

⇒ b² = 4 x 5

⇒ b² = 20

Thus, the equation of the hyperbola is x²/25 - y²/20 = 1

---

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 12

Find the equation of the hyperbola satisfying the given conditions: Foci (± 3√5, 0), the latus rectum is of length 8

Summary:

The equation of the hyperbola is x²/25 - y²/20 = 1 while the Foci is (± 3√5, 0) and the latus rectum is of length 8