# How do you find the equation for a circle with a center at (1,2) that passes through the point (-2,-1)?

Jan 4, 2016

If it passes thru $\left(- 2 , - 1\right)$, then use the distance formula to find the radius (r) ...

#### Explanation:

radius $r = \sqrt{{\left(1 - \left(- 2\right)\right)}^{2} + {\left(2 - \left(- 1\right)\right)}^{2}} = \sqrt{18}$

The general equation for a circle is:

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

where, center $= \left(h , k\right) = \left(1 , 2\right)$

Now, since we know the value of $h , k , \mathmr{and} r$ ...

${\left(x - 1\right)}^{2} + {\left(y - 2\right)}^{2} = {\left(\sqrt{18}\right)}^{2} = 18$

hope that helped