What is the standard form of a circle's equation?
Understand the Problem
The question is asking for the standard form of a circle's equation, which is a fundamental concept in geometry related to the relationship between a circle's center and radius.
Answer
The standard form of a circle's equation is $ (x  h)^2 + (y  k)^2 = r^2 $.
Answer for screen readers
The standard form of a circle's equation is given by:
$$(x  h)^2 + (y  k)^2 = r^2$$
Steps to Solve

Identify the circle's center and radius
You need to determine the center of the circle and the radius. In the standard form of a circle's equation, which is given by:
$$ (x  h)^2 + (y  k)^2 = r^2 $$
Here, $(h, k)$ is the center and $r$ is the radius. 
Substitute the values into the formula
Replace $h$, $k$, and $r$ in the standard form equation with the respective values. For example, if the center is at $(3, 2)$ and the radius is $5$, the equation would become:
$$ (x  3)^2 + (y + 2)^2 = 5^2 $$ 
Simplify the equation
Finally, calculate $r^2$ and simplify the equation. Continuing the example:
$$ (x  3)^2 + (y + 2)^2 = 25 $$
The standard form of a circle's equation is given by:
$$(x  h)^2 + (y  k)^2 = r^2$$
More Information
The standard form of a circle's equation is very useful in geometry and analytic geometry. It helps you determine critical properties of the circle such as its center and radius quickly.
Tips
 Misidentifying the center: Make sure to correctly identify $(h, k)$ from the coordinates provided.
 Incorrectly calculating $r^2$: Always square the radius correctly. For example, if the radius is 4, $r^2$ must be 16, not 12 or any other number.