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Chapter 2: Problem 34

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(2,-1), r=4$$

Short Answer

Expert verified
The standard form of the equation of the circle is \( (x - 2)^2 + (y + 1)^2 = 16 \)

Step by step solution

01

Identify the Center and Radius

The center of the circle is given as \( (2, -1) \) and the radius as \( 4 \). This means our \( h \) is 2, \( k \) is -1, and \( r \) is 4.
02

Substitute Center and Radius into Standard Formula

We replace \( h, k, \) and \( r \) in the standard form equation all at once. This will give us the equation: \( (x - 2)^2 + (y - (-1))^2 = 4^2 \)
03

Simplify Equation

Simplify the equation to its final form: \( (x - 2)^2 + (y + 1)^2 = 16 \)

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