Solids of revolution Consider the ellipse x2 + 4y2 = 1 in

Chapter 12, Problem 80E

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QUESTION:

Solids of revolution  Consider the ellipse \(x^{2}+4 y^{2}=1\) 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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QUESTION:

Solids of revolution  Consider the ellipse \(x^{2}+4 y^{2}=1\) 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:

Solution  80E

The equation of an ellipse in standard form is += 1

Here a is referred to as the length of the horizontal semi-axis and b is the length of the vertical semi-axis. An ellipse is standard form is always centered at the origin

Graph tof ellipse shown below

Consider the ellipse in the xy-plane

= 1

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