# How do you find general form of circle with center at the point (5,7); tangent to the x-axis?

Jan 26, 2016

${\left(y - 7\right)}^{2} + {\left(x - 5\right)}^{2} = 49$

#### Explanation:

The general form of a circle is ${\left(y - k\right)}^{2} + {\left(x - h\right)}^{2} = {r}^{2}$
where $\left(h , k\right)$ is the centre of the circle and $r$ is the radius.

Because the circle is tangent to the $x$ axis and the $y$ coordinate of the centre is $7$, the radius $r = 7$ - see sketch.

So the equation becomes
${\left(y - 7\right)}^{2} + {\left(x - 5\right)}^{2} = {7}^{2}$

${\left(y - 7\right)}^{2} + {\left(x - 5\right)}^{2} = 49$