# How do you write the equation of the circle with center and radius (1,-3), 10?

##### 1 Answer
Jul 3, 2016

${\left(x - 1\right)}^{2} + {\left(y + 3\right)}^{2} = 100$

#### 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.

in this question a = 1 , b = -3 and r = 10

Substitute these values into the standard equation.

${\left(x - 1\right)}^{2} + {\left(y - \left(- 3\right)\right)}^{2} = {10}^{2}$

$\Rightarrow {\left(x - 1\right)}^{2} + {\left(y + 3\right)}^{2} = 100 \text{ is the equation}$