Foci, (±3√5,0), the latus ** 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
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.
∴b2 = 4a = 4 × 5 = 20
Thus, the equation of the hyperbola is X2/25 - y2/20 =1.
