How do you find the center and radius of the circle #-2x^2 - 2y^2 + 24x - 54 = 0#?

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Answer 1 · 2016-12-03T17:46:14

This is a circle, center #(6,0)# and radius #3#

Rearrange the equation to look like

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

This is a circle center #(a,b)# and radius #r#

Dividing by #-2#

#x^2-12x+y^2=-27#

Completing the squares

#x^2-12x+36+y^2=-27+36#

#(x-6)^2+y^2=9=3^2#

so this is a circle, center #(6,0)# and radius #3#

graph{-2x^2-2y^2+24x-54=0 [-2.64, 13.16, -3.416, 4.49]}