What is the center and radius of the circle #x^2+y^2-2x+4y-4=0#?

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Answer 1 · 2017-03-10T08:45:49

centre#" "(1,-2)#

radius#" "3#

The standard eqn of a circle with centre #(a,b)# and radius #r#

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

for #" "x^2+y^2-2x+4y-4=0" "#we need to complete the square.

#" "x^2+y^2-2x+4y-4=0" "#

#color(red)(x^2-2x)+color(blue)(y^2+4y)-4=0#

#color(red)((x^2-2x+1^2))+color(blue)((y^2+4y+2^2))-1^2-2^2-4=0#

#color(red)((x-1)^2)+color(blue)((y+2)^2)-9=0#

#(x-1)^2+(y+2)^2=9#

centre#" "(1,-2)#

radius#" "sqrt9=3#