# How do you find the standard form of the equation of the hyperbola given the properties foci #(+-5,0)#, length of the conjugate axis 6?

##### 1 Answer

Please see the explanation.

#### Explanation:

Because the foci are given to be

We know that

Substitute the value for "b" into equation [1]:

We know that the general forms for the foci are:

This allows us to write the following equations:

Substitute the value for k into equation [2]:

Find the value of h by adding equations [4] and [5]:

Substitute into equation [6]:

Use equation [5] to find the value of "a":

#25 = a^2+9

Substitute the value of "a" into equation [7]

Equation [8] is the equation of the hyperbola.