How do you find the equation of an ellipse with foci #(+-5,0)# and major axis of length 12?
Please see the 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:
We are given that the major axis is length 12, therefore, we substitute 6 for "a" into equation :
The foci for this type of ellipse are located at:
Using the foci,
Add equations  and :
Subtract equation  from equation :
Substitute these values into equation :