Find the equation of the hyperbola whose foci are `(pm5,0)` and vertices are `(pm3,0)`.

Explanation

Since the foci on the x-axis, the equation of the hyperbola is of the form `(x^(2))/(a^(2))-(y^(2))/(b^(2)) =1`.
Since, vertices are `(pm3, 0)`, therefore a = 3 i.e., `a^(2) = 9`
Also, since foci are `(pm5, 0)`, therefore c = 5
Now, `b^(2) = c^(2) - a^(2)`
`rArr b^(2) = 25 - 9`
`rArr b^(2) =- 16`
Therefore, the equation of the hyperbola is `(x^(2))/(9) - (y^(2))/(16) = 1`.