Question

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

Answer 1

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

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.