Question

Answer the following:

Find the equation of the hyperbola in the standard form if length of the conjugate axis is 3 and distance between the foci is 5.

Answer 1

Let the required equation of hyperbola be

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

Length of conjugate axis = 2b

Given, length of conjugate axis = 3

∴ 2b = 3

∴ b = `3/2`

∴ b² = `9/4`

Distance between foci = 2ae

Given, distance between foci = 5

∴ 2ae = 5

∴ ae = `5/2`

∴ a²e² = `25/4`

Now, b² = a²(e² – 1)

∴ b² = a²e² – a²

∴ `9/4 = 25/4` – a²

∴ a² = `25/4 - 9/4`

∴ a² = `16/4` = 4

∴ The required equation of hyperbola is

`x^2/4 - y^2/((9/4))` = 1,

i.e., `x^2/4 - (4y^2)/9` = 1