# How do you write an equation for a circle with center (2,0) and radius sqrt11?

Apr 24, 2016

${x}^{2} - 4 x + {y}^{2} - 7 = 0$

#### Explanation:

The equation of a circle is

${x}^{2} + {y}^{2} = {r}^{2}$,

where $r$ is the radius, given as $\sqrt{11}$, so

${x}^{2} + {y}^{2} = {\sqrt{11}}^{2} = 11$.

You want to get the circle centered around the origin $\left(0 , 0\right)$, which you do by adding or subtracting a certain amount to the $x$ and $y$ values of the center to get it to $0$.

$x$ is given as $2$ (the point is $\left(2 , 0\right)$), so you subtract $2$. $y$ is $0$ so you can leave it the same. This gives an equation of

${\left(x - 2\right)}^{2} + {y}^{2} = 11$.

Expanding this out,

${x}^{2} - 4 x + 4 + {y}^{2} = 11$

${x}^{2} - 4 x + {y}^{2} - 7 = 0$