How do you find the center and radius of the circle given #x^2+y^2+8x-6y=0#?

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Answer 1 · 2017-01-12T09:09:15

This is the equation of a circle, center #(-4,3)# and radius #=5#

We need

#(a+b)^2=a^2+2ab+b^2#

#(a-b)^2=a^2-2ab+b^2#

Complete the squares for the x and y

#x^2+y^2+8x-6y=0#

#x^2+8x+y^2-6y=0#

#x^2+8x+color(red)((8/2)^2)+y^2-6y+color(blue)((6/2)^2)=color(red)((8/2)^2)+color(blue)((6/2)^2)#

#x^2+8x+color(red)((4)^2)+y^2-6y+color(blue)((3)^2)=color(red)((4)^2)+color(blue)((3)^2)#

#(x+4)^2+(y-3)^2=25=5^2#

This is the equation of a circle, center #(-4,3)# and radius #=5#

graph{(x^2+y^2+8x-6y)=0 [-15.25, 13.23, -3.42, 10.82]}