The equation of circle in the xy-plane is #x^2+y^2+4x-2y = -1#. What is the radius of the circle?

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Answer 1 · 2017-01-17T08:41:55

radius #=2#

The standard equation of a circle with centre #(a,b),#and radius # r#
is: #(x-a)^2+(y-b)^2=r^2#

so for : # x^2+y^2+4x-2y=-1# we will have to complete the square before we can identify the radius.

# x^2+y^2+4x-2y=-1#

# x^2+4x+y^2-2y=-1#

#( x^2+4x)+(y^2-2y)=-1#

#( x^2+4x+2^2)-2^2+(y^2-2y+1^2)-1^2=-1#

#(x+2)^2-4+(y-1)^2-1=-1#

#(x+2)^2+(y-1)^2=-1+1+4#

#(x+2)^2+(y-1)^2=4#

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

radius#=sqrt4=2#

for good measure centre #(-2,1)#