Equation of a Circle (WJEC Eduqas GCSE Maths: Higher): Revision Note

• if asked for the radius, don't forget to square root r²

  • e.g. for x² + y² = 10, the radius is √10, not "10"

The diagram shows a circle, centred on the origin.

(a) Write down the equation of the circle.

Answer:

Identify the radius by checking where the circle crosses the coordinate axes

$r=5$

Substitute this into $x^2+y^2=r^2$

$x^2+y^2=5^2$

$x^2+y^2=25$

(b) Does the point $P\left(3,4\right)$ lie on, inside or outside the circle? You must show working to support your answer.

Answer:

Substitute $x=3$ and $y=4$ into $x^2+y^2$

$\begin{array}{rcl}{x}^2+y^2& =& 3^2+4^2\\ & =& 9+16\\ & =& 25\end{array}$

Since $3^2+4^2=25$, the point $P\left(3,4\right)$ lies on the circle