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

Finding the centre and radius from the equation of a circle is easy.## How to Find the Centre from the Equation of a Circle

Find the Cartesian coordinates of the centre of the circle from the equation.## Question

What is the centre 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

In our example, it is

**− 1**.## 3

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

The
−1 → 1

**x-coordinate**of the centre 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

In our example, it is

**+ 2**.## 6

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

The
+ 2 → − 2

**y-coordinate**of the centre of the circle is

**−2**.

## Answer:

The centre of the circle with the equation**(x − 1)**is:

^{2}+ (y + 2)^{2}= 9## 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

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)**is

^{2}+ (y + 2)^{2}= 9**3**. The circle with the equation

**(x − 1)**has centre

^{2}+ (y + 2)^{2}= 9**(1, −2)**and radius

**3**.

## Top Tip

## The Center of a Circle

The equation of a circle is:The center is

**(a, b)**.

- The number being subtracted from the
**x**in the brackets is the x-coordinate of the center. - The number being subtracted from the
**y**in the brackets is the y-coordinate of the center.

**(−1, 2)**. The equation will start:

(x − −1)

Remember, that subtracting a negative number is the same as adding the positive number:
^{2}+ ...
(x

A negative coordinate will have a **− −1**)^{2}= (x**+ 1**)^{2}**+**sign in front of it. A positive coordinate will have a

**−**sign in front of it. With practise, it is straightforward to read off the center of the circle.

## Beware

## Equations That Don't Quite Look Right

Don't be confused if you see an equation which looks like this:
(x − 1)

This is still an equation of a circle, as can be seen with a little rearranging:
^{2}+ (y − 3)^{2}− 49 = 0
(x − 1)

^{2}+ (y − 3)^{2}= 49## You might also like...

graphs and coordinate geometryunderstanding the equation of a circleunderstanding the equation of a circle in general formconverting an equation of a circle from general to standard form

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