Question

Find the equation of the hyperbola referred to its principal axes:

whose distance between foci is 10 and length of conjugate axis 6

Answer 1

Let the equation of the hyperbola referred to its principal axes be

`x^2/"a"^2 - y^2/"b"^2` = 1     ...(1)

Distance between foci = 2ae = 10

Length of conjugate axis = 2b = 6

∴ ae = 5 and b = 3

b² = a²(e² – 1) = a²e² – a²

∴ 3² = 5² – a²

∴ a² = 25 – 9 = 16

∴ by (1), the equation of the required hyperbola is `x^2/16 - y^2/9` = 1.