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Match the equation with its graph (labeled I-VIII). Give reasons for your choice.

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

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$I$

02:00

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Missouri State University

Harvey Mudd College

University of Nottingham

Idaho State University

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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Match the equation with it…

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So for 26 we want to match the equation with its graph. Um, and in this case, the equation that we have the graph that were given is y squared equals X squared plus two z squared. So what we can do is we can use traces. So if we let Z equal K, then what will end up getting? Is that why squared minus X squared equals two k squared. So these traces are obviously hyperbole as so. What that means is that when we let Z be constant, the X and Y plane is going to be is going to show hyperbole eyes. Then if y equals K um, so we just have the xz plane. Then what we end up getting is that k squared equals X squared plus two z squared. And this would obviously be ellipses then lastly, we let x equal k and we end up getting y squared minus two z squared equals k squared. And these are also hyperbole us. So, based on this, looking at the different traces that we have, um, we see that 12 and three are possible traces, But since 000 is a point on this surface, only one is going to have it. So our answer for this graph is going to be one mhm.

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