Question

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

whose length of transverse axis is 8 and distance between foci is 10

Answer 1

Let the required equation of hyperbola be

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

Length of transverse axis = 2a

Given, length of transverse axis = 8

∴ 2a = 8

∴ a = 4

∴ a² = 16

Distance between foci = 2ae

Given, distance between foci = 10

∴ 2ae = 10

∴ ae = `10/2` = 5

∴ a²e² = 25

Now, b² = a²(e² – 1)

∴ b² = a²e² – a²

∴ b² = 25 – 16 = 9

∴ The required equation of hyperbola is `x^2/16 - y^2/9` = 1.