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Find an equation for the surface obtained by rotating the line $ z = 2y $ about the z-axis.

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$x^{2}+y^{2}=\frac{z^{2}}{4}$

01:14

Wen Zheng

01:10

Carson Merrill

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Missouri State University

Harvey Mudd College

Baylor University

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Find an equation for the s…

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Find the equation of the s…

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in this problem, it is asked to find any question for the surface obtained by rotating the line that equals to two by about the by access. So, what does it mean? We have considered a book. Mhm. That is very equal to white. All right. So, now this curve is rotated about said access. That means this is nothing. But we need to replace. Why by That is why that is given to us. That is by route over its square place. Why is that? Right? So we need to do just one. So here this becomes very simple for the equation for the resulting surface will be what when we rotate about their access? Right? So this will this becomes is there any questions to root X squared plus Y. Is well, as we have already told that why will become at a square place twice favorite? Yeah. So, this will be given by This is four. We are just squaring it. Yes. So there's become four X squared plus Y square. And this side left inside becomes that square. So this becomes that's where is equal to four X squared plus poor race. But so this is the resulting equation for us. So this is how we solve this problem. I hope your industry, the concept. Thank you for watching.

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