# How do you write an equation for a circle given center (4,2) and tangent to the x-axis?

Oct 30, 2016

Please see the explanation.

#### Explanation:

The standard form of the equation of a circle is:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

where $\left(h , k\right)$ is the center point and r is the radius

Substitute the center point $\left(4 , 2\right)$ into the standard form:

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

Because the center is 2 units above the x axis and the circle is tangent to the x axis, the radius must be 2:

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