**Graph the Circle**The equation of the circle is given by:\[(x + 1)^2 + (y + 4)^2 = 16\]To graph the circle, use the graphing tool located on the right. Click to enlarge the graph for a better view of its details.*Graph Description*: The image includes a small button labeled "Click to enlarge graph," featuring an icon of a graph with a circular plot, indicating interactivity for users to better view and manipulate the graph for educational purposes.

Answered: Graph the circle. x+12+42 = 16 42=D Use…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

**Graph the Circle**

The equation of the circle is given by:

\[
(x + 1)^2 + (y + 4)^2 = 16
\]

To graph the circle, use the graphing tool located on the right. Click to enlarge the graph for a better view of its details.

*Graph Description*: The image includes a small button labeled "Click to enlarge graph," featuring an icon of a graph with a circular plot, indicating interactivity for users to better view and manipulate the graph for educational purposes.

Expert Solution

Step 1

the given equation is:

${(x + 1)}^{2} + {(y + 4)}^{2} = 16$

the above equation can be written as:

$\begin{array}{rcl} {(x + 1)}^{2} + {(y + 4)}^{2} & = & 16 \\ {(x - (- 1))}^{2} + {(y - (- 4))}^{2} & = & 4^{2} \end{array}$

as we know the equation of the circle having centre at (h,k ) and radius r is:

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

therefore compare the equation ${(x - (- 1))}^{2} + {(y - (- 4))}^{2} = 4^{2}$ with the equation ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

therefore, h=-1, k=-4 and r=4.

therefore ${(x + 1)}^{2} + {(y + 4)}^{2} = 16$ is the equation of the circle having centre at (-1,-4) and radius equal to 4.

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Graph the circle. x+12+42 = 16 42=D Use the graphing tool on the right to graph the circle. Click to enlarge graph