In each of the, find the equations of the hyperbola satisfying the given conditions.

Foci ( 3, 0), the latus rectum is of length 8.

Foci ( 3, 0), the latus rectum is of length 8.

Here, the foci are on x-axis.

Thus,

The equation of the hyperbola is of the form

Since, the foci are (), c=

Length of latus rectum = 8

⇒

⇒ b² = 4a

We know that, a² + b² = c²

a² + 4a = 45

⇒ a² + 4a -45 = 0

⇒ a² + 9a – 5a -45 = 0

⇒ (a +9)(a -5) = 0

⇒ A = -9,5

Since, a is non – negative, a = 5

Thus, b² = 4a = 4 × 5 = 20

Hence, the equation of the hyperbola is