# How do you find the center of the radius of (x-1)^2 + (y+2)^2 =25?

Jul 11, 2016

centre = (1 ,-2) and radius = 5

#### 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.

The equation ${\left(x - 1\right)}^{2} + {\left(y + 2\right)}^{2} = 25 \text{ is in this form}$

and by comparison with the standard form we obtain.

a = 1 , b = -2 and r = 5

Hence centre = (a ,b) = (1 ,-2) and radius = 5