# How do you find the center and radius of a circle using a polynomial (x - 3) ^2 + (y + 4) ^2 = 25?

Apr 30, 2018

$\text{centre "=(3,-4)" and radius } = 5$

#### Explanation:

$\text{the equation of a circle in standard form is}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(a,b)" are the coordinates of the centre and r}$
$\text{is the radius}$

${\left(x - 3\right)}^{2} + {\left(y + 4\right)}^{2} = 25 \text{ is in this form}$

$\text{with centre "=(3,-4)" and radius } = \sqrt{25} = 5$