In order to write down the equation of a circle you will need to know two things:

**1)** First you will need to know the coordinates of the centre of the circle. We shall call the centre of the circle (a,b).

**2)** The second thing you will need is the radius of the circle. This is normally referred to as r.

Once you have these two pieces of information you can substitute these values into the following formula:

**(x – a)² + (y-b)² = r²**

This will be your final answer for the equation of a circle.

**Example 1**

A circle has a centre of (3,6) and a radius of 4. Write down the equation of the circle.

The centre of the circle is at (3,6) so a=3 and b=6.

Also since the radius is 4 then r = 4.

All you need to do now is put these values into the formula above.

(x – a)² + (y-b)² = r²

(x – 3)² + (y-6)² = 4²

Which simplifies to:

(x – 3)² + (y-6)² = 16

There is no need to expand the brackets on the left hand side of the equation unless the question specifies you to write down the equation in a different form.

**Example 2**

A circle has a centre of (2,-5) and a radius of 7. Write down the equation of the circle.

The centre of the circle is at (2,-5) so a=2 and b=-5.

Also since the radius is 7 then r = 7.

All you need to do now is substitute these values into the formula above.

Be careful with the negative signs.

(x – a)² + (y-b)² = r²

(x – 2)² + (y- -5)² = 7²

Which simplifies to:

(x – 2)² + (y+5)² = 49

Again there is now need to expand the brackets out.

**Extra Help:**

Writing down the equation of a circle in the form x² + y² + dx + ey + f = 0.

Working out the radius and centre of the circle from the equation of a circle.