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Sketch and identify a quadric surface that could have the traces shown.

Traces in $ x = k $Traces in $ z = k $

This is a one-sheeted hyperboloid

02:52

Wen Z.

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

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In mathematics, a vector (…

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Sketch and identify a quad…

02:59

Use traces to sketch and i…

00:49

03:56

Sketch the appropriate tra…

02:35

03:36

02:44

05:28

01:41

03:10

So, um, for this problem, we want to look at when x is constant. When x is constant, we see we get the equation of the form P Y squared plus Q Z squared equals one. Lindsay is constant. We get something of the form M X squared minus and Y squared equals one. And therefore we have an equation of the surface that's of the form a X squared minus B y squared plus C Z squared equals one, and that's going to be a one sheeted hyperba, Lloyd. So the way we make sense of this is if we have, um, our Z axis and then we have the Y axis, and then we have our X axis. What we end up seeing is that this sheet will be in such a way that it opens up here, and then it kind of has this hourglass shaped like this. So that would be our one sheeted hyper Boyd

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Use traces to sketch and identify the surface.

$ x = y^2 - z^2 $

$ y = z^2 - x^2 $

Sketch the appropriate traces, and then sketch and identify the surface.…

$ x = y^2 + 4z^2 $