Question

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

whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)

Answer 1

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

`x^2/"a"^2 - y^2/"b"^2` = 1    ...(1)

Then vertices are (±a, 0) which are given to be (±7, 0).

∴ a = 7

Also, end points of conjugate axes are (0, ±b) which are given to be (0, ±3).

∴ b = 3

∴ by (1), the equation of required hyperbola is `x^2/49 - y^2/9` = 1.