How do you write the equation of the circle in standard form, identify the center and radius of #x^2+y^2-10x-6y+25=0#?

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Answer 1 · 2017-02-22T14:22:09

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

We rewrite the equation by completing the squares

#x^2+y^2-10x-6y+25=0#

#(x^2-10x)+(y^2-6y)=-25#

#(x^2-10x+25)+(y^2-6y+9)=-25+25+9#

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

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

graph{(x^2+y^2-10x-6y+25)((x-5)^2+(y-3)^2-0.003)=0 [-4.97, 12.81, -1.88, 7.01]}