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

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.

c^{2}=a^{2}-b^{2}

5^{2}=7^{2}-b^{2}

b^{2}=7^{2}-5^{2}=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