Final answer:
The equation when the ellipse is centered at the origin, has axes of lengths 8 and 4, and its major axis horizontal is b. (x^2/64 +y^2/16 = 1 )
Step-by-step explanation:
To write the equation of the ellipse with the given information, we can use the general equation for an ellipse centered at the origin:
(x^2/a^2) + (y^2/b^2) = 1
Based on the information provided, the semimajor axis (a) is 8 and the semiminor axis (b) is 4.
Since the major axis is horizontal, the larger value (a) corresponds to the x-axis and the smaller value (b) corresponds to the y-axis. Therefore, the correct equation is:
(x^2/64) + (y^2/16) = 1
The answer is option b. This equation represents an ellipse centered at the origin, with axes of lengths 8 and 4, and a horizontal major axis.