# How do you write the equation for a circle centered at (h,k) = (5,-8) and passing through the point (3,-2)?

Aug 8, 2018

${\left(x - 5\right)}^{2} + {\left(y + 8\right)}^{2} = 40$

#### Explanation:

$\text{the standard form of the equation of a circle is}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the centre and r}$
$\text{is the radius}$

$\text{the radius r is the distance from the centre to the point}$
$\text{on the circumference}$

$\text{calculate r using the "color(blue)"distance formula}$

•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

$\text{let "(x_1,y_1)=(5,-8)" and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 2\right)$

$r = \sqrt{{\left(3 - 5\right)}^{2} + {\left(- 2 + 8\right)}^{2}} = \sqrt{4 + 36} = \sqrt{40}$

${\left(x - 5\right)}^{2} + {\left(y + 8\right)}^{2} = 40 \leftarrow \textcolor{b l u e}{\text{is equation of circle}}$