Derive the equation of the ellipse with foci at (1,0) and (−1,0) whose distance between vertices is 6. Make a picture to help. Label the foci, and place and label a point (x, y) along the ellipse. Draw the focal distances from the point (x, y) to each focus point.

Hint: Note that the endpoints on the major axis are often called vertices (the other endpoints on the minor axis are called co-vertices).

Use the fact that the distance between the vertices is equal to the sum of the focal distances. Use the distance formula to start.

Put the steps in order: