Final answer:
The endpoints of the major axis of the ellipse are (2,9) and (2,-3), while the endpoints of the minor axis are (5.46,3) and (-1.46,3), with the ellipse centered at (2,3).
Step-by-step explanation:
To identify the endpoints of the major axis and minor axis of the ellipse given by the equation (x-2)²/12 + (y-3)²/36=1, we need to understand the structure of the ellipse. Here, the denominators of the fractions give us the squares of the lengths of the semi-major and semi-minor axes. Therefore, the length of the semi-major axis is √36, which is 6, and the length of the semi-minor axis is √12, which is about 3.46.
The ellipse is centered at (2,3). The major axis is along the y-axis, and the minor axis is along the x-axis due to the larger denominator being under the (y-3)² term. Thus, the endpoints of the major axis are (2,3+6) and (2,3-6), which simplifies to (2,9) and (2,-3). Similarly, the endpoints of the minor axis are (2+3.46,3) and (2-3.46,3), which simplifies to (5.46,3) and (-1.46,3).