# How do you find the equation of the circle given center (0,0) and the radius 10?

Jul 9, 2016

${x}^{2} + {y}^{2} = 100$

#### Explanation:

The standard form of the equation of a circle is.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where (a ,b) are the coordinates of the centre and r, the radius.

here a = 0 , b = 0 and r = 10

Substitute these values into the standard equation.

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {10}^{2}$ which simplifies to

$\Rightarrow {x}^{2} + {y}^{2} = 100 \text{ is the equation of the circle}$