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Q. 36

Expert-verified

Geometry

Found in: Page 527

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

In Exercises 35-38 find an equation of the circle described and sketch the graph.
The circle has center (-2, -4) and passes through point (3, 8).

The equation of the circle is ${(x + 2)}^{2} + {(y + 4)}^{2} = 169$

The graph is:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step-1 – Given

Given that the circle has center = (-2, -4) and passes through the point (3, 8).

Step-2 – To determine

We have to find the equation of the circle and sketch the graph.

Step-3 – Calculation

We first find the length of the radius by finding the distance between (-2, -4) and (3, 8).

$\begin{array}{l} r = \sqrt{{(3 - (- 2))}^{2} + {(8 - (- 4))}^{2}} \\ r = \sqrt{{(3 + 2)}^{2} + {(8 + 4)}^{2}} \\ r = \sqrt{{(5)}^{2} + {(12)}^{2}} \\ r = \sqrt{25 + 144} \\ r = \sqrt{169} \\ r = 13 \end{array}$

Here, center = (a, b) = (-2, -4) and radius = r = 13.

We plug them in the standard form of the equation of a circle:

${(x - a)}^{2} + {(y - b)}^{2} = r^{2}$

${(x + 2)}^{2} + {(y + 4)}^{2} = 13^{2}$

${(x + 2)}^{2} + {(y + 4)}^{2} = 169$

So, the equation of the circle is ${(x + 2)}^{2} + {(y + 4)}^{2} = 169$ .

Step-4 – Graph

We will sketch the graph using a graphing utility.

Step 1: Press WINDOW button in order to access the Window editor.

Step 2: Press $Y=$ button.

Step 3: Enter the expression ${(x + 2)}^{2} + {(y + 4)}^{2} = 169$ .

Step 4: Press GRAPH button to graph the function and then adjust the window.

The obtained graph is:

From the graph, we see that the center is (-2, -4) and the radius is 13.

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