What type of conic section is given by the equation 4x2 + 9y2 = 36? What are its domain and range?
The given equation 4x^2 + 9y^2 = 36 represents an ellipse.
The domain of the ellipse is all real numbers for x, and the range is all real numbers for y.
In terms of the nature of the ellipse, it is centered at the origin (0, 0), with the x-axis as the major axis and the y-axis as the minor axis. The vertices of the ellipse are at (-3, 0) and (3, 0), and the co-vertices are at (0, -2) and (0, 2). The foci of the ellipse are at (-√5, 0) and (√5, 0).