The Equation of a Circle

In this tutorial you are shown how the equation of a circle is derived when you know the centre and radius.

You will also be taken through this example.

(1)

Find the equation of a circle with centre (4, -2) and radius 3 which you may want to try as part of your revision before looking at the video.

Tutorial on finding the equation of a circle and worked solution to (1)

 

Finding the Centre and Radius from another form of the Equation of a Circle

You should be aware of the alternative form of the equation of a circle and how you can find the centre and radius.

(2)

In this tutorial I show you how to find the centre and radius from the following equation of a circle

x²+y²+10x-12y+9=0

Tutorial on the alternative form of the equation of a circle and worked solution to (2)

 

Finding the Equation of a Tangent

In this tutorial you are shown how to find the equation of a tangent to a circle from this example.

(3)

Find the equation of the tangent to the circle x²+y²+10x+2y+13=0 at the point (-3, 2)

Tutorial and Worked Solution to (3)

 

Finding the Equation of a Circle given 3 points on the Circumference

In the first tutorial I introduce you to the method I use and then a simple example.

(4)

Find the equation of the circle passing through the points (-1,5), (3,5) and (3,-1).

In the next example I take this further and consider a harder example.

(5)

Find the equation of a tangent passing through the points (-2,2), (5,1) and (-2, -6)

Tutorial and Worked Solution to (4) and (5)