# How to Find the Center and Radius from the Equation of a Circle

## Finding the Center and Radius from the Equation of a Circle

We can find the center and the radius of a circle from the equation of a circle.

Imagine we wanted to find the center and radius of the circle with the equation:

## How to Find the Center and Radius from the Equation of a Circle

Finding the center and radius from the equation of the circle is easy.

### How to Find the Center from the Equation of a Circle

Find the Cartesian coordinates of the center of the circle from the equation.

### Question

What is the center of the circle with the equation **(x − 1) ^{2} + (y + 2)^{2} = 9**?

### Step-by-Step:

# 1

Find the brackets with the **x** in it.

# 2

Look at the number in these brackets and the sign in front of it.

In our example, it is **− 1**.

# 3

Change the sign of the answer (−1) to find the x-coordinate of the center of the circle.

−1 → 1

The **x-coordinate** of the center of the circle is **1**.

# 4

Find the brackets with the **y** in it.

# 5

Look at the number in these brackets and the sign in front of it.

In our example, it is **+ 2**.

# 6

Change the sign of the answer (+2) to find the y-coordinate of the center of the circle.

+ 2 → − 2

The **y-coordinate** of the center of the circle is **−2**.

### Answer:

The center of the circle with the equation **(x − 1) ^{2} + (y + 2)^{2} = 9** is:

### How to Find the Radius from the Equation of a Circle

Find the radius of the circle from the equation.

### Question

What is the radius of the circle with the equation **(x − 1) ^{2} + (y + 2)^{2} = 9**?

### Step-by-Step:

# 1

Find the number not in brackets. It is usually written to the right of the equals sign (=).

In our example, it is **9**.

# 2

Find the square root of the answer (9).

√9 = 3

### Answer:

The radius of the circle with the equation **(x − 1) ^{2} + (y + 2)^{2} = 9** is

**3**.

The circle with the equation **(x − 1) ^{2} + (y + 2)^{2} = 9** has center

**(1, −2)**and radius

**3**.