Question

Consider the ellipse 25xsquared plus 4y squared equals 1 in the​ xy-plane. a. If this ellipse is revolved about the​ x-axis, what is the equation of the resulting​ ellipsoid? b. If this ellipse is revolved about the​ y-axis, what is the equation of the resulting​ ellipsoid?

Answer 1

• about x: 25x² +4y² + 4z² = 1
• about y: 25x² +4y² +25z² = 1

Explanation:

When the figure is revolved around the x-axis, its extent in the z-direction will match its extent in the y-direction. So, the z-term will have the same coefficient as the y-term. 25x² +4y² +4z² = 1

Similarly, when the figure is revolved around the y-axis, its extent in the z-direction will match its extent in the x-direction. Then the z-term will have the same coefficient as the x-term. 25x² +4y² +25z² = 1