Question

In Exercises $83-86,$ determine whether each statement makes sense or does not make sense, and explain your reasoning. You told me that an ellipse centered at the origin has vertices at $(-5,0)$ and $(5,0),$ so I was able to graph the ellipse.

Name: Problem 85, Chapter 7: College Algebra
Uploaded: 2020-06-11T22:04:02-08:00
Duration: 1 min 24 s
Channel: Carrie Hicks
Description: In Exercises 83-86, determine whether each statement makes sense or does not make sense, and explain your reasoning. You told me that an ellipse centered at the origin has vertices at (-5,0) and (5,0), so I was able to graph the ellipse.

   In Exercises $83-86,$ determine whether each statement makes sense or does not make sense, and explain your reasoning.
You told me that an ellipse centered at the origin has vertices at $(-5,0)$ and $(5,0),$ so I was able to graph the ellipse.

College Algebra

Robert Blitzer 7th Edition

Chapter 7, Problem 85

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Solved by Expert Carrie Hicks

06/11/2020

Step 1

The statement mentions an ellipse centered at the origin with vertices at $(-5,0)$ and $(5,0)$. This information is crucial because it tells us the ellipse is horizontally oriented (since the vertices are along the x-axis) and the center of the ellipse is at the Show more…

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In Exercises $83-86,$ determine whether each statement makes sense or does not make sense, and explain your reasoning. You told me that an ellipse centered at the origin has vertices at $(-5,0)$ and $(5,0),$ so I was able to graph the ellipse.

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Key Concepts

Ellipse Properties

An ellipse is a conic section defined as the set of points for which the sum of the distances from two fixed points (the foci) is constant. Its defining features include its center, vertices (the endpoints of the major axis), co-vertices (the endpoints of the minor axis), and foci. Understanding these features is crucial when determining the correct equation and properties of the ellipse.

Graphing Conic Sections

Graphing an ellipse typically involves using its center, vertices, and co-vertices to accurately render its shape and orientation. While knowing the vertices (especially if the ellipse is centered at the origin) is important, complete and accurate graphing requires full information about both the major and minor axes. This ensures that the shape of the ellipse is depicted properly according to its standard equation.

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