The equation of a circle is x^2+y^2-4x+10y = -20, what are the co-ordinates of the center and the length of the radius of the circle?

Jan 15, 2016

centre = (2 , - 5 ) and radius = 3

Explanation:

The general form of the equation of a circle is:

${x}^{2} + {y}^{2} + 2 g x + 2 f y + c = 0$

in this question : ${x}^{2} + {y}^{2} - 4 x + 10 y + 20 = 0$

comparing the coefficients : 2g = - 4 $\Rightarrow g = - 2$

$2 f = 10 \Rightarrow f = 5 \mathmr{and} c = 20$

centre = ( - g , - f ) = (2 , - 5 )

and $r = \sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{\left(- 2\right)}^{2} + {5}^{2} - 20}$

$\Rightarrow r = \sqrt{4 + 25 - 20} = \sqrt{9} = 3$