Practice!

Sample Problem

Find the standard form of the equation of the ellipse with foci (-7, 2) and (3, 2) and major axis of length 14.

Solution

Because the foci occur at (-7, 2) and (3, 2), the center of the ellipse must be ([-7+3]/2, 2)=(-2, 2) and the distance from the center to one of the foci is c=5. Because 2a=14, we also know that a=7.

c2=a2-b2

52=72-b2

b2=72-52=49-25=24

b=√24

Because the two foci share the same y-coordinate, we know the major axis is horizontal and the equation of this ellipse is therefore