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Question
Find the equation of the hyperbola satisfying the given conditions:
Foci (±5, 0), the transverse axis is of length 8.
Solution
Foci (±5, 0), the transverse axis is of length 8.
Here, the foci are on the x-axis.
Therefore, the equation of the hyperbola is of the form `x^2/a^2 - y^2/b^2 = 1`
Now, Foci are (±5, 0), c = 5.
Length of transverse axis 8, 2a = 8 = a = 4.
We know that a2 + b2 = c2.
Therefore, 42 + b2 = 52
b2 = 25 - 16 = 9
Thus, the equation of the hyperbola is = `x^2/16 - y^2/9 = 1`
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