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Chapter 42: Chapter 42

Problem 724

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Write an equation for the circle with center \(\mathrm{A}(-3,-2)\) and radius 3.

Short Answer

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\((x + 3)^2 + (y + 2)^2 = 9\)
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify the center and radius of the circle

The center of the circle, \((x_0, y_0)\), is given as \(\mathrm{A}(-3, -2)\), and the radius, \(r\), is given as 3.

Step 2: Use the standard formula for a circle

The standard formula for a circle is \((x - x_0)^2 + (y - y_0)^2 = r^2\). Plug in the values for the center and radius that we identified in Step 1: \((x + 3)^2 + (y + 2)^2 = 3^2\).

Step 3: Simplify the equation

Simplify the equation: \((x + 3)^2 + (y + 2)^2 = 9\). This is the equation of the circle with center \(\mathrm{A}(-3, -2)\) and radius 3.

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