# How do you find the equation of the circle with radius 6 and center (2,4)?

Apr 16, 2016

I found: ${x}^{2} + {y}^{2} - 4 x - 8 y - 16 = 0$

#### Explanation:

You can use the general relationship for the equation of a circle of center at $\left(h , k\right)$ and radius $r$ as:

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

${\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = {6}^{2}$
${x}^{2} - 4 x + 4 + {y}^{2} - 8 y + 16 = 36$
${x}^{2} + {y}^{2} - 4 x - 8 y - 16 = 0$

Apr 16, 2016

${\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = 36$

#### 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 = 2 , b = 4 and r = 6

substitute these values into the standard equation

$\Rightarrow {\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = 36 \text{ is the equation }$