The foci are horizontally aligned (they have the same y-coordinate), so the ellipse is horizontal.

General equation for a horizontal ellipse:

 (x-h)²/a² + (y-k)²/b² = 1

with

 a ≥ b

 center (h,k)

 vertices (h±a,k)

 co-vertices (h,k±b)

 foci (h±c,k), c² = a² - b²

Apply the given information and solve for h, k, a, b, and c.

(h,k) = (4,4)

h = k = 4

foci (h±c, k) = (4±7,4)

c = 7

a = 3c = 21

a² = 441

c² = a² - b²

7² = 21² - b²

b² = 21² - 7² = 392

The equation becomes

(x-4)²/441 + (y-4)²/392 = 1