# How do you find the center and radius of the circle (x-4)^2 + (y)^2 = 25?

May 22, 2016

centre (4 ,0) , r = 5

#### Explanation:

The equation of a circle in standard form 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) is the centre and r ,the radius.

For ${\left(x - 4\right)}^{2} + {y}^{2} = 25$

by comparison with standard a = 4 , b = 0 and r = 5

$\Rightarrow \text{centre"=(4,0)" and radius} = 5$