# How do you find the equation of a circle with centre (5,4) and just touches the x-axis?

Jul 20, 2016

The equation of a circle with centre in $\left(a , b\right)$ and radius $r$ is ${\left(x - a\right)}^{2} + \left(y - {b}^{2}\right) = {r}^{2}$

#### Explanation:

We know that the centre is $\left(a , b\right) = \left(5 , 4\right)$, so we only need to find out the radius. But the circle 'just touches' the x-axis, so the distance of the centre to the x-axis is 4 (see the figure):

graph{(x-5)^2+(y-4)^2=16 [-5.79, 14.21, -1.16, 8.84]}

Then the radius is 4, and the equation is:

${\left(x - 5\right)}^{2} + {\left(y - 4\right)}^{2} = 16$