# How do you write the equation of the circle with center at ( 5, -2) and diameter of 8?

Aug 3, 2018

The eqn. of circle is :

${x}^{2} + {y}^{2} - 10 x + 4 y + 25 = 0$

#### Explanation:

The equation of circle with center at $\left(h , k\right)$ and radius of $r$ is :

color(red)((x-h)^2+(y-k)^2=r^2

We have center $\left(5 , - 2\right) \mathmr{and} \text{radius } r = \frac{8}{2} = 4$

So ,the eqn. of circle is :

${\left(x - 5\right)}^{2} + {\left(y - \left(- 2\right)\right)}^{2} = {\left(4\right)}^{2}$

$\implies {x}^{2} - 10 x + 25 + {y}^{2} + 4 y + 4 = 4$

$\implies {x}^{2} + {y}^{2} - 10 x + 4 y + 25 = 0$

Aug 3, 2018

${\left(x - 5\right)}^{2} + {\left(y + 2\right)}^{2} = 16$

#### Explanation:

Recall that the equation of a circle is given by

$\overline{\underline{|} \textcolor{w h i t e}{\frac{2}{2}} {\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2} \textcolor{w h i t e}{\frac{2}{2}} |}$, with center $\left(h , k\right)$ and radius $r$.

We are centered at $\left(5 , - 2\right)$, which means $h = 5$ and $k = 2$.

We also know that we have a diameter of $8$, which means our radius is $4$.

We have all of the information we need, so we can now write the equation of this circle.

${\left(x - 5\right)}^{2} + {\left(y + 2\right)}^{2} = 16$

Hope this helps!