The Ellipse - Problem 7

An ellipse equation needs to be in standard form, meaning equal to one with two perfect square binomials, in order for us to find any key features that are based on the values of "a," "b," and/or "c." In this case, there are no linear terms for x or y, which tells us that the ellipse is centered at the origin. Hence, there is no need to complete the square. Rather, we divide all terms by what is on the right side, 64, in order to make the ellipse equal to one. From there, our new denominators represent a^2 and b^2. Using the relation a^2 - b^2 = c^2, we can solve for c in order to find the coordinates of the foci.