Foci (± 3,0), the latus rectum is of length.

Given: foci are (± 3,0), c = 3

and length of latus rectum = = 8

As b² = 4a

We have c² = a² + b²

or 45 = a² + 4a

or a² + 4a – 45 = 0

or a² + 9a – 5a - 45 = 0

or a(a + 9) –5(a – 9) = 0

or (a + 9) (a – 5) = 0

or a = -9 or a = 5)

since a cannot be negative, we take a = 5 and so b² = 20.

Therefore, the equation of the required hyperbola is

= 1 ⇒ 4x² – 5y² = 100.