Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find an equation for the circle with center at the point $(- 5, 1)$ and radius 3. Graph this circle.

The equation of the circle is $\begin{array}{rcl} {(x + 5)}^{2} + {(y - 1)}^{2} & = & 9 \end{array}$ .
The graph is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The center of the circle is $(- 5, 1)$ .
The radius is 3.

Step 2. Find the Equation

The general equation of a circle is ${(x - h)}^{2} + {(x - k)}^{2} = r^{2}$ .
Substitute $h = - 5, k = 1$ into the general equation and simplify.

localid="1647407263863" $\begin{array}{rcl} (x - {(- 5))}^{2} + {(y - 1)}^{2} & = & 3^{2} \\ {(x + 5)}^{2} + {(y - 1)}^{2} & = & 9 \end{array}$

Step 3. Find the Intercepts

Substitute 0 for x and find the y-intercepts.

$\begin{array}{rcl} {(0 + 5)}^{2} + {(y - 1)}^{2} & = & 9 \\ {(y - 1)}^{2} & = & - 16 \end{array}$

As the square is a negative value, there are no x-intercepts.
Substitute 0 for y and find the x-intercepts.

$\begin{array}{rcl} {(x + 5)}^{2} + {(0 - 1)}^{2} & = & 9 {(x + 5)}^{2} = 8 x + 5 = \pm 2 \sqrt{2} \\ x & = & - 2 \sqrt{2} - 5, - 2 \sqrt{2} + 5 \end{array}$

Step 4. Plot the Graph

Use the center and the intercepts to plot the circle.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find an equation for the circle with center at the point $(- 5, 1)$ and radius 3. Graph this circle.

Step by Step Solution

Step 1. Given Information

Step 2. Find the Equation

Step 3. Find the Intercepts

Step 4. Plot the Graph

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find an equation for the circle with center at the point (-5,1) and radius 3. Graph this circle.

Step by Step Solution

Step 1. Given Information

Step 2. Find the Equation

Step 3. Find the Intercepts

Step 4. Plot the Graph

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Find an equation for the circle with center at the point $(- 5, 1)$ and radius 3. Graph this circle.