A **circle** is the collection of points that are equidistant to a center point. The distance is the **radius** denoted *r*. The **center** is denoted .

The **standard form of an equation of a circle** is where *r* is the radius and is the center.

**Example**: Find the center and the radius from the given equation.

Solution: If you line up the standard form of a circle with the equation given you can determine the center and the radius.

In the binomial with x, the number after the minus sign is h. Thus, . In the binomial with y, the number after the minus sign is k. Thus, . The lines up with 16. So which means .

This is the equation of a circle with a center of and a radius of .

**Example**: Find the center and the radius from the given equation.

Solution: Notice that one of the binomials has a + instead of the – that is in the standard form of the circle. Rewrite the addition as subtraction.

is the same as .

The rewritten equation is as follows.

Then, if you line up the standard form of a circle with the equation given you can determine the center and the radius.

In the binomial with x, the number after the minus sign is h. Thus, . In the binomial with y, the number after the minus sign is k. Thus, . The lines up with 25. So which means .

This is the equation of a circle with a center of and a radius of .

**Example**: Find the center and the radius from the given equation.

Solution: Notice that one of the binomials has a + instead of the – that is in the standard form of the circle. Rewrite the addition as subtraction.

is the same as .

The other binomial doesn’t have any number added or subtracted. We can rewrite this by subtracting zero.

is the same as .

The rewritten equation is as follows.

Then, if you line up the standard form of a circle with the equation given you can determine the center and the radius.

In the binomial with x, the number after the minus sign is h. Thus, . In the binomial with y, the number after the minus sign is k. Thus, . The lines up with 25. So which means .

This is the equation of a circle with a center of and a radius of .