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Chapter 2: Problem 40

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-2,0), r=6$$

Short Answer

Expert verified
The standard form of the equation of the circle is \( (x + 2)^2 + y^2 = 36 \).

Step by step solution

01

Identify the parameters

It's given that the center of the circle is (-2,0) and the radius is 6. In terms of the standard equation for a circle, \( h = -2\), \( k = 0\), and \( r = 6 \).
02

Substitute parameters into the equation

Substitute \( h = -2\), \( k = 0\), and \( r = 6 \) into the standard equation which is \( (x - h)^2 + (y - k)^2 = r^2 \). By doing so, you get \( (x - (-2))^2 + (y - 0)^2 = 6^2 \).
03

Simplify the equation

Simplify the equation to get its final form. This results in \( (x + 2)^2 + y^2 = 36 \).

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