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प्रश्न
Find the equation of the hyperbola satisfying the given conditions:
Vertices (0, ±5), foci (0, ±8)
उत्तर
Vertices (0, ±5), foci (0, ±8)
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, ±5), a = 5.
Since the foci are (0, ±8), c = 8.
We know that a2 + b2 = c2.
∴ 52 + b2 = 82
b2 = 64 - 25 = 39
Thus, the equation of the hyperbola is `y^2/25 - x^2/39 = 1`.
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