# How do you write an equation for a circle given center (-8,7) and radius is 1/2 units?

Jul 10, 2017

${\left(x + 8\right)}^{2} + {\left(y - 7\right)}^{2} = \frac{1}{4}$

#### Explanation:

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

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

$\text{where " (a,b)" are the coordinates of the centre and}$
$\text{r the radius}$

$\text{here " (a,b)=(-8,7)" and } r = \frac{1}{2}$

$\Rightarrow {\left(x - \left(- 8\right)\right)}^{2} + {\left(y - 7\right)}^{2} = {\left(\frac{1}{2}\right)}^{2}$

$\Rightarrow {\left(x + 8\right)}^{2} + {\left(y - 7\right)}^{2} = \frac{1}{4} \text{ is the equation}$

Jul 10, 2017

${\left(x + 8\right)}^{2} + {\left(y - 7\right)}^{2} = \frac{1}{4}$

#### Explanation:

The standard form for an equation of a circle is given by

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

where

• $h$ is the $x$-coordinate for the center of the circle

• $k$ is the $y$-coordinate for the center of the circle

• $r$ is the radius of the circle

Plugging In known values, we have

${\left(x - \left(- 8\right)\right)}^{2} + {\left(y - \left(7\right)\right)}^{2} = {\left(\frac{1}{2}\right)}^{2}$

color(red)((x+8)^2 + (y-7)^2 = 1/4