Question

Find the equation of the hyperbola centered at the origin that has a vertex at (5, 0) and a focus at (9, 0).

Answer 1

Refer to the diagram shown below.

The vertex is at (a,0), with a = 5.
The focus is at (c,0), with c = 9.
Therefore
b² = c² - a² = 81 - 25 = 56

The equation of the hyperbola is

`(x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1, \\ or \\ (x^(2))/(25) - (y^(2))/(56)=1`

Answer:

`(x^(2))/(25) - (y^(2))/(56) =1`