# How do you find the equation of the circle given center at (7, 0) and a radius of 10?

Jul 19, 2016

${\left(x - 7\right)}^{2} + {y}^{2} = 100$

#### 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 centre = (7 ,0) hence a = 7 , b = 0 and r = 10.

Substitute these values into the standard equation.

${\left(x - 7\right)}^{2} + {\left(y - 0\right)}^{2} = {10}^{2}$

$\Rightarrow {\left(x - 7\right)}^{2} + {y}^{2} = 100 \text{ is the equation of the circle}$