# How do you write the general form of a circle given characteristics. Center: (−5, 1); solution point: (0, 0)?

Dec 19, 2015

${\left(x + 5\right)}^{2} + {\left(y - 1\right)}^{2} = 26$

#### Explanation:

A circle of radius $r$, centered at $\left(h , k\right)$ has the form

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

From the given information, we have $h = - 5$ and $k = 1$. To find $r$, we need only find the distance from the center $\left(h , k\right)$ to a point on the circle. As $\left(0 , 0\right)$ is such a point, applying the distance formula gives us

$r = \sqrt{{\left(- 5 - 0\right)}^{2} + {\left(1 - 0\right)}^{2}} = \sqrt{26}$

Thus the desired equation is

${\left(x - \left(- 5\right)\right)}^{2} + {\left(y - 1\right)}^{2} = {\sqrt{26}}^{2}$

or, simplifying,

${\left(x + 5\right)}^{2} + {\left(y - 1\right)}^{2} = 26$