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Reduce the equation to one of the standard forms, classify the surface, and sketch it.

$ y^2 = x^2 + \frac{1}{9} z^2 $

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01:05

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Johns Hopkins University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

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.

05:44

Reduce the equation to one…

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02:44

All right. We want to write the standard form of execution, which is like it's already in the standard form and this is an elliptic corn. And the reason for this is the following. So let's draw the accesses again again for the sake of convenience and draw. This is my Y axis. This is my thanks. And this is magic. So jimmy. The story of here. Is that so you for any money of why I'm always positive. And if I fix anyone I'd say why is one, then this is one equal to access square, Just 1/90 schools. But this is an ellipse. Similarly at Y equals two while also getting her lips. But at a bigger Like just 40 close to excess where personal overlying. So every time my anti access a bigger. So really? So what is happening here? Is that every time I I got this for each point at each exit plan, I'm really in the lips. So at each this this is an ellipse that rejects the plan on at least, and similarly, the same story happens below. So, right. So each of these things here sections releases some of that story is usually similar stories here, so that is why this is an elliptical.

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