Identify the type of conic section that has the equation 9x^2 + 16y^2 = 144 and identify its domain and range.
The given equation 9x^2 + 16y^2 = 144 represents an ellipse.
The general form of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Comparing the given equation with the general form, we have:
a^2 = 16, so a = 4
b^2 = 9, so b = 3
Therefore, the semi-major axis is along the x-axis and has a length of 2a = 8, and the semi-minor axis is along the y-axis and has a length of 2b = 6.
The center of the ellipse is at the origin (0,0).
The domain of the ellipse is all real numbers for x, and the range of the ellipse is -6 ≤ y ≤ 6.