Question

Use traces to sketch and identify the surface 36x² y² 36z²=36

A. Ellipsoid
B. Hyperboloid
C. Sphere
D. Cone

Answer 1

To identify the surface represented by the equation 36x² y² 36z²=36, we can use traces. Traces are obtained by fixing one of the variables (x, y, or z) and graphing the resulting equation in the remaining variables. Let's fix x=0 and plot the equation 0² y² 36z²=36. Simplifying, we get y² + 36z² = 36. This is the equation of an ellipse, so the surface is an ellipsoid. The correct answer is A. Ellipsoid.

Step-by-step explanation:

To identify the surface represented by the equation 36x² y² 36z²=36, we can use traces. Traces are obtained by fixing one of the variables (x, y, or z) and graphing the resulting equation in the remaining variables.

Let's fix x=0 and plot the equation 0² y² 36z²=36. Simplifying, we get y² + 36z² = 36. This is the equation of an ellipse, so the surface is an ellipsoid.

Therefore, the correct answer is A. Ellipsoid.