# How do you write an equation for a circle with center (3,5) tangent to the x-axis?

May 11, 2016

${\left(x - 3\right)}^{2} + {\left(y - 5\right)}^{2} = {5}^{2}$. Expansion gives ${x}^{2} + {y}^{3} - 6 x - 10 y + 9 = 0$

#### Explanation:

x-axis touches the circle. So, the altitude from the center is the a

radius of the circle. The altitude is center's y-coordinate = 5.

So, the equation of the circle is

${\left(x - 3\right)}^{2} + {\left(y - 5\right)}^{2} = {5}^{2}$. Expansion gives

${x}^{2} + {y}^{3} - 6 x - 10 y + 9 = 0$