# How do you write the equation for a circle with Origin: (5,5) ; Radius = 2?

Jun 11, 2016

${x}^{2} + {y}^{2} - 10 x - 10 y + 46 = 0$.

#### Explanation:

The equation of the circle is

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

Where ${c}_{x}$ and ${c}_{y}$ are the coordinates of the center and $r$ is the radius.

Then we have

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

${x}^{2} - 10 x + 25 + {y}^{2} - 10 y + 25 = 4$

${x}^{2} + {y}^{2} - 10 x - 10 y + 50 = 4$

${x}^{2} + {y}^{2} - 10 x - 10 y + 46 = 0$.