# Find the equation of the circle centered at (3,-4) and radius =5?

Jun 21, 2018

${\left(x - 3\right)}^{2} + {\left(y + 4\right)}^{2} = 25$

#### Explanation:

The equation of a circle can be written as

${\left(x - {x}_{0}\right)}^{2} + {\left(y - {y}_{0}\right)}^{2} = {r}^{2}$

Where $\left({x}_{0} , {y}_{0}\right)$ is the center, and $r$ is the radius.

In this case you have all the information you need, so you just need to plug the values: given $\left({x}_{0} , {y}_{0}\right) = \left(3 , - 4\right)$ and $r = 5$ you have

${\left(x - 3\right)}^{2} + {\left(y + 4\right)}^{2} = 25$

Jun 21, 2018

color(green)(" Equation of the circle is " (x - 3)^2 + (y + 4)^2 = 5^2

#### Explanation:

$\text{Equation of a circle } {\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

$\text{Given : } h = 3 , k = - 4 , r = 5$

:. color(green)(" Equation of the circle is " (x - 3)^2 + (y + 4)^2 = 5^2