# What is the standard form of the equation of a circle passing through Center at the point (1, 0) and has the point (-2, 3)?

Aug 3, 2017

${\left(x - 1\right)}^{2} + {y}^{2} = 18$

#### Explanation:

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

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

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

$\text{the radius is the distance from the centre to } \left(- 2 , 3\right)$

$\Rightarrow r = \sqrt{{\left(- 2 - 1\right)}^{2} + {\left(3 - 0\right)}^{2}} = \sqrt{18}$

$\Rightarrow {\left(x - 1\right)}^{2} + {y}^{2} = 18 \text{ is the equation}$