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Question
Find the equation of the hyperbola satisfying the given conditions:
Vertices (0, ±3), foci (0, ±5)
Solution
Vertices (0, ±3), foci (0, ±5)
Here, the vertices are on the y-axis.
Therefore, the equation of the hyperbola is of the form `y^2/a^2 - x^2/b^2 = 1`
Since the vertices are (0, ±3), a = 3.
Since the foci are (0, ±5), c = 5.
We know that a2 + b2 = c2.
∴ 32 + b2 = 52
= b2 = 25 - 9 = 16
Thus, the equation of the hyperbola is `y^2/9 - x^2/16 = 1`.
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