The standard equation of the ellipse is as follows:
where (h,k) is the coordinates of the center.
Since the y-coordinates of the foci are the same, the formula for the foci is as follows:
Thus, to obtain the value of c, equate the x-coordinates to h+c and h-c and then solve for c.
Add the two equations and then solve for h.
Since h=1, substitute the value of h into h+c and solve for c.
Since the vertex is (-7,2), the value of k is 2. Equate the -7 to h-a and then solve for a.
Substitute the value of a and c into the following equation and then solve for b².
Obtain the value of a².
Identify the coordinates of the center.