What are the foci of the ellipse 8x^2 + 12y^2 = 96?
This can be rewritten as x^2/12 + y^2/8 = 1. Note that a^2=12 and b^2=8, and since a^2=b^2+c^2 in an ellipse, we know that c^2=4 and consequently c=2. Since the ellipse is centered at the origin, we know the foci are located at (-2, 0) and (2, 0). (Since x^2 is divided by a larger number than y^2 in the modified equation of the ellipse, we know that the x-axis is the major axis of this ellipse, and so the foci must lie on the x-axis as indicated above.
