# 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?

# 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?

# 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. ## Slider

The slider below shows another real example of how to find the center and radius from the equation of a circle.

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## See Also

What is an equation? What is a circle? What are Cartesian coordinates? What is the x-coordinate? What is the y-coordinate?