Question

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

x squared over 8 plus y squared over 4 equals 1
x squared over 16 plus y squared over 4 equals 1
x squared over 8 minus y squared over 4 equals 1
x squared over 16 minus y squared over 4 equals 1

Answer 1

The equation of the ellipse is x²/16 + y²/4 = 1.

Step-by-step explanation:

The equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (-2, 0) can be determined by using the formula for an ellipse in standard form: (x-h)²/a² + (y-k)²/b² = 1. In this formula, (h, k) represents the center of the ellipse and a and b represent the semi-major and semi-minor axes, respectively.

We can see that the center of the ellipse is at (0, 0) since the directrices are at x = ±4. The distance between the center and each focus is equal to c, which is 2 (since the foci are at (2, 0) and (-2, 0)).

Therefore, the equation of the ellipse is x²/16 + y²/4 = 1.