Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (-2, 0) ?

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