Final answer:
The equation 9y^2 + z^2 = 36 represents an ellipse in three-dimensional space with a center at the origin (0, 0, 0). The major axis is parallel to the z-axis and the minor axis is parallel to the y-axis. The semi-major axis of the ellipse is 6 units and the semi-minor axis is 2 units.
Step-by-step explanation:
The equation 9y^2 + z^2 = 36 represents an ellipse in three-dimensional space. The major axis of the ellipse is parallel to the z-axis, while the minor axis is parallel to the y-axis. The center of the ellipse is at the origin (0, 0, 0). The equation can be rewritten as (y/2)^2/2^2 + z^2/6^2 = 1, which represents an ellipse with a semi-major axis of length 6 and a semi-minor axis of length 2.
The graph of the equation 9y^2 + z^2 = 36 is an ellipse centered at the origin with a semi-major axis length of 6 along the z-axis and a semi-minor axis length of 2 along the y-axis.
To determine the graph of the equation 9y^2 + z^2 = 36, we need to recognize the type of graph that this equation represents. Dividing through by 36, we rewrite the equation as y^2/4 + z^2/36 = 1, which is the equation of an ellipse in the yz-plane, with the y-axis and z-axis being its axes. The length of the semi-major axis along the z-axis is 6, while the semi-minor axis length along the y-axis is 2. The correct graph would show an ellipse centered at the origin with these axes' lengths.