# How do you write the equation for a hyperbola given vertices (-5,0) and (5,0), conjugate axis of lengths 12 units?

##### 1 Answer

Nov 11, 2016

Please see the explanation for steps leading to the equation:

#### Explanation:

The two vertices have the same y coordinate, therefore, the hyperbola is the horizontal transverse axis type. The standard equation for the horizontal transverse axis type is:

We know that the general form for the vertices of this type are:

Using the given vertices

Solve for h and a:

From the reference, the length of the conjugate axis is equal to 2b:

We know the values of h, k, a, and b, substitute them into the general form: