Question

Find the equation of the hyperbola with centre at the origin, length of conjugate axis 10 and one of the foci (–7, 0).

Answer 1

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.