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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).
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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