How do use the method of translation of axes to sketch the curve #x^2+y^2+2x-6y+6=0#?

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Answer 1 · 2017-01-24T17:40:44

See the method below

We rewrite the equation by completing the squares

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

#(x^2+2x+1)+(y^2-6y+9)=-6+9+1#

#(x+1)^2+(y-3)^2=4#

This is a circle, center #(-1,3)# and radius #=2#

We define new axes

#x'=x+1#

and #y'=y-3#

#(x')^2+(y')^2=4#

This is a circle, center #(0,0)# and radius #=2#

graph{((x+1)^2+(y-3)^2-4)(x^2+y^2-4)=0 [-10, 10, -5, 5]}