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miss Akunina [59]
3 years ago
11

Consider the ellipse 25xsquared plus 4y squared equals 1 in the​ xy-plane. a. If this ellipse is revolved about the​ x-axis, wha

t 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?
Mathematics
1 answer:
BaLLatris [955]3 years ago
5 0

Answer:

  • 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

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