Answer:
x^2/8 + y^2/4 = 1
Step-by-step explanation:
As the diretrix are vertical lines, we have a horizontal ellipse, which equation is:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
As the foci are at (2,0) and (-2,0), we have that k = 0, h = 2-2 = 0 and c = 2, where c^2 = a^2 - b^2
As the diretrix are in x = ±4, we have that d = 4, where:
c / a = a / d
So now we can find a:
2 / a = a / 4
a^2 = 8
a = 2.828
And then we can find b:
2^2 = 2.828^2 - b^2
b^2 = 2.828^2 - 2^2 = 4
b = 2
So the ellipse equation is:
x^2/8 + y^2/4 = 1
