# What is the standard form of the equation of a circle with center (0,0) and whose radius is 5?

Jun 20, 2018

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$ this is the general form of the equation of a circle with centre $\left(a , b\right)$ and radius $r$

Putting you values in

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {5}^{2}$

${x}^{2} + {y}^{2} = 25$

Jun 20, 2018

${x}^{2} + {y}^{2} = 25$

#### Explanation:

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

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

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

$\text{here "(a,b)=(0,0)" and } r = 5$

${\left(x - 0\right)}^{2} + {\left(y = 0\right)}^{2} = {5}^{2}$

${x}^{2} + {y}^{2} = 25 \leftarrow \textcolor{red}{\text{equation of circle}}$