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?

Question

Mathematics

Myah Brown

9 May, 23:33

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?

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Elaine Rose · Answer 1

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

Step-by-step 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