# How do you write the equation for a circle with center C(7,-4) and passes through P(-3,3)?

Nov 18, 2016

#### Explanation:

The standard equation for a circle is:

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

where $\left(x , y\right)$ is any point on the circle, $\left(h , k\right)$ is the center, and r it the radius.

GIven the center is $\left(7 , - 4\right)$, substitute for h and k in the general form:

${\left(x - 7\right)}^{2} + {\left(y - - 4\right)}^{2} = {r}^{2}$

Note: I do not recommend that you change the second term to be ${\left(y + 4\right)}^{2}$; doing so can cause confusion, when asked for the center.

To find the value of r substitute the given point:

${\left(- 3 - 7\right)}^{2} + {\left(3 - - 4\right)}^{2} = {r}^{2}$

${r}^{2} = 149$

$r = \sqrt{149}$

The equation is:

${\left(x - 7\right)}^{2} + {\left(y - - 4\right)}^{2} = {\left(\sqrt{149}\right)}^{2}$