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प्रश्न
Find the equation of the hyperbola with centre at the origin, length of conjugate axis 10 and one of the foci (–7, 0).
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उत्तर
Let the equation of the hyperbola be `x^2/"a"^2 - y^2/"b"^2` = 1 ...(1)
Length of conjugate axis = 2b = 10
∴ b = 5
One of the focus is (– ae, 0)
It is given to be (– 7, 0)
∴ ae = 7
b2 = a2(e2 – 1) = a2e2 – a2
∴ 52 = 72 – a2
∴ a2 = 49 – 25 = 24
∴ by (1), the equation of the hyperbola is `x^2/24 - y^2/25` = 1.
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