# How do you find the equation of an ellipse with foci #(+-5,0)# and major axis of length 12?

##### 1 Answer

Please see the explanation.

#### Explanation:

Because the x coordinate of the foci is the coordinate that is changing, we know that the major axis of the ellipse is parallel to the x axis. Therefore, the standard Cartesian form of the equation of the ellipse is:

where

We are given that the major axis is length 12, therefore, we substitute 6 for "a" into equation [1]:

The foci for this type of ellipse are located at:

Using the foci,

Add equations [3] and [4]:

Subtract equation [3] from equation [4]:

Substitute these values into equation [2]: