# How do you find the coordinates of the center of the circle x^2 +y^2 -4x+ 6x =12?

Mar 11, 2016

$r = \frac{7}{2}$

#### Explanation:

${x}^{2} + {y}^{2} - 4 x + 6 x = 12$
${x}^{2} + {y}^{2} + 2 x - 12 = 0$
${x}^{2} + {y}^{2} + D x + E y + F = 0$
$C \left(a , b\right) \text{ center coordinates}$
$D = 2 \text{ "E=0" } F = - 12$
$a = - \frac{D}{2} = - \frac{2}{2} = - 1$
$b = - \frac{E}{2} = \frac{0}{2} = 0$
$r = \frac{1}{2} \cdot \sqrt{{D}^{2} + {E}^{2} - 4 \cdot F}$
$r = \frac{1}{2} \cdot \sqrt{{\left(- 1\right)}^{2} + 0 + 4 \cdot 12}$
$r = \frac{1}{2} \cdot \sqrt{1 + 48}$
$r = \frac{1}{2} \cdot \sqrt{49}$
$r = \frac{7}{2}$