How do you find the center and radius of (x - 5) ^2 + (y + 3)^ 2 = 25?

Sep 18, 2016

centre = (5 ,-3) 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.

${\left(x - 5\right)}^{2} + {\left(y + 3\right)}^{2} = 25 \text{ is in this form}$

and by comparison with the standard form.

$a = 5 , b = - 3 \text{ and } {r}^{2} = 25 \Rightarrow r = \sqrt{25} = 5$

Hence centre = (5 ,-3) and radius = 5