Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

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Solution

Vertices (0, ±5), foci (0, ±8)

Here, the vertices are on the y-axis.

Therefore, the equation of the hyperbola is of the form.

Since the vertices are (0, ±5), a = 5.

Since the foci are (0, ±8), c = 8.

We know that a² + b² = c².

Thus, the equation of the hyperbola is.

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