EDUCATIONAL GURU MATH: Circle basics

Circle basics

You must be able to recognise when an equation represents a circle.

Any equation of the form

will represent a circle, provided at least one of p, q and r is not zero.

The general equation of a circle normally appears in the form

where (-g, -f) is the centre of the circle and $\sqrt {g^2 + f^2 - c}$ is the radius.

Notice that for the circle to exist

.

Look at the following worked examples.

For

so equation represents a circle with centre = (-3, 4) and radius $= \sqrt {36} = 6$

For

does not represent a circle.

For

we must write this starting

like this:

$\eqalign{ x^2 + y^2 - 2x + {1 \over 3}y - 3 = 0\cr\cr g^2 + f^2 - c = ( - 1)^2 + ({1 \over 6})^2 - ( - 3) = 4{1 \over {36}} = {{145} \over {36}}\cr$

so equation represents a circle with centre = $(1, - {1 \over 6})$ and radius $\sqrt {{{145} \over {36}}} = {{\sqrt {145} } \over 6}$