# 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?

##### 1 Answer

Jan 15, 2016

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

#### Explanation:

The general form of the equation of a circle is:

#x^2 + y^2 + 2gx + 2fy + c = 0 # in this question :

#x^2 + y^2 - 4x + 10y + 20 = 0# comparing the coefficients : 2g = - 4

#rArr g = - 2 #

#2f = 10 rArr f = 5 and c = 20 # centre = ( - g , - f ) = (2 , - 5 )

and

#r = sqrt(g^2 + f^2 - c ) = sqrt((-2)^2 + 5^2 - 20 )#

#rArr r = sqrt(4 + 25 - 20 ) = sqrt9 = 3 #