Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

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asked Feb 10, 2018 in Mathematics by Rohit Singh (61,782 points) 36 146 472
Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

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answered Feb 10, 2018 by sameer (82,980 points) 5 14 70

Vertices (±2, 0), foci (±3, 0)
Here, the vertices are on the x-axis.

Therefore, the equation of the hyperbola is of the form X2/a2 - Y2/b2 =1.
Since the vertices are (±2, 0), a = 2.
Since the foci are (±3, 0), c = 3.
We know that a2 + b2 = c2.

Thus, the equation of the hyperbola is X2/4 - Y2/5 =1.

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