# How do you find the equation for a hyperbola centered at the origin with a horizontal transverse axis of lengths 8 units and a conjugate axis of lengths 6 units?

##### 1 Answer

The equation is:

#### Explanation:

Using this reference Conics: Hyperbola, the general equation for a hyperbola with a transverse horizontal axis is:

where

We are given that the center is,

We are given that the length of the horizontal transverse axis is 8; this allows us to write this equation:

Substitute 4 for "a" in equation [2]:

We are given that the length of the horizontal transverse axis is 6; this allows us to write this equation:

Substitute 3 for "b" in equation [3]: