Solution Found!
Solids of revolution Consider the ellipse x2 + 4y2 = 1 in
Chapter 12, Problem 80E(choose chapter or problem)
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?
Questions & Answers
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