Find the equation of the hyperbola satisfying the give conditions: Foc – InterviewSolution

1.	Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.
Answer» Foci (0, ±13), the conjugate axis is of length 24. Here, the foci are on the y-axis. Therefore, the equation of the hyperbola is of the form Y²/a² - x²/b² =1. Since the foci are (0, ±13), c = 13. Since the length of the conjugate axis is 24, 2b = 24 ⇒ b = 12. We know that a² + b² = c². ∴a² + 12² = 13² ⇒ a² = 169 – 144 = 25 Thus, the equation of the hyperbola is Y²/25 - X²/144 =1.

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