Explanation:
The standard form equation of an ellipse with horizontal major axis, centered at the origin and with foci at (±c, 0) and directrices at x = ±a is:
x^2 / a^2 + y^2 / (a^2 - c^2) = 1
Comparing with the given information, we have:
a = 4 (since the directrices are at x = ±4)
c = 2 (since the foci are at (2, 0) and (-2, 0))
Substituting these values in the equation of the ellipse, we get:
x^2 / 16 + y^2 / (16 - 4) = 1
x^2 / 16 + y^2 / 12 = 1
Multiplying both sides by 16 * 12, we get:
12x^2 + 16y^2 = 192
Dividing both sides by 192, we get:
x^2 / 16 + y^2 / 12 = 1
This is in the standard form of the equation of an ellipse, so the answer is (B) x squared over 16 plus y squared over 4 equals 1.