What are the coordinates of the center and the length of the radius of the circle represented by the equation #x^2+y^2-4x+8y+11=0#?

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Answer 1 · 2017-06-02T09:28:11

Center #C=(2;-4)#, radius #r=3#

To find the radius and center we have to transform the equation to

#(x-a)^2+(y=b)^2=r^2#

#x^2+y^2-4x+8y+11=0#

#x^2-4x+4-4+y^2+8y+16-16+11=0#

#(x-2)^2-4+(y+4)^2-16+11=0#

#(x-2)^2+(y+4)^2-9=0#

#(x-2)^2+(y+4)^2=9#

From the transformed equation we can see that the circle's center is #C=(2;-4)# and radius #r=3#