Question

Graph the equation: $x^2+y^2=9$

Name: Problem 3, Chapter 10: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-06-15T23:54:06-08:00
Duration: 1 min 39 s
Channel: Vicki Stebbins
Description: Graph the equation: x^2+y^2=9

   Graph the equation: $x^2+y^2=9$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 10, Problem 3

Instant Answer

Solved by Expert Vicki Stebbins

06/15/2020

Step 1

The given equation is $x^2 + y^2 = 9$. This is the equation of a circle in standard form, $x^2 + y^2 = r^2$, where $r$ is the radius of the circle. Show more…

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Graph the equation: $x^2+y^2=9$

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Key Concepts

Circle Equation

This concept involves understanding that the equation x² + y² = r² represents a circle centered at the origin with radius r. In a standard Cartesian coordinate system, the equation of a circle is expressed in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Center and Radius

The center and radius are key elements in the graphing process of a circle. Here, identifying the center as (0, 0) and the radius as the square root of the constant term allows one to accurately determine the location and size of the circle on the graph.

Graphing Methods

Graphing equations involves plotting the recognized features such as the center and the distance equal to the radius in all directions. This fundamental process is applicable to various conic sections and helps in visualizing their geometric shapes on the coordinate plane.

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