The Ellipse - Problem 11

Even if you are not explicitly asked to sketch a graph of an ellipse, drawing a rough sketch will help you orient the major axis and give you a sense of how the given points are related. Here, we know the center and a vertex (which will tell us the "a" value and whether the major axis is vertical or horizontal, ) and covertex (which will tell us the "b" value). These distances will help us decide whether the x^2 term is over a^2 (if major axis is horizontal) or over b^2 (if major axis is vertical). An ellipse equation will always equal one. The last piece we are asked to find is the foci: we use the relationship a^2 - b^2 = c^2 to find c and calculate that distance from the center along the major axis to locate the foci.