# How do you write the standard from of the equation of the circle given center (2, 3) and radius 4?

Sep 9, 2016

${\left(x - 2\right)}^{2} + {\left(y - 3\right)}^{2} = 16$

#### 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 the centre = (2 ,3) hence a = 2 , b=3 and r = 4

substitute these values into the standard form of the equation.

$\Rightarrow {\left(x - 2\right)}^{2} + {\left(y - 3\right)}^{2} = 16 \text{ is the equation of the circle}$