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Chapter 1: Problem 71

Write the standard form of the equation of the circle with the given characteristics. Center: \((2,-1) ;\) Radius: 4

Short Answer

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

Step by step solution

01

Identify the values

Given the problem, the coordinates of the center are \((a, b) = (2, -1)\). The radius \(r\) is 4. These values need to be substituted into the standard form equation of the circle.
02

Substitute the values into the equation

Substitute \((a, b)\) and \(r\) into the equation. The equation becomes \((x-2)^2 + (y - (-1))^2 = 4^2\).
03

Simplify the equation

After substitution, the equation is \((x-2)^2 + (y + 1)^2 = 16\). No further simplification is required as this is the standard form.

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