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Question
Find the equation of the hyperbola satisfying the given conditions:
Foci (0, ±13), the conjugate axis is of length 24.
Solution
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 `y^2/a^2 - x^2/b^2 = 1`
Now foci are (0, ±13), c = 13.
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 `y^2/25 - x^2/144 = 1`.
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