How do you classify the conic #x^2+y^2-2x+6y+9=0#?

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Answer 1 · 2016-11-30T15:50:28

We have a a circle, center #(1,-3)# and radius #=1#

The general equation of a conic is

#Ax^2+Bxy+Cy^2+Dx+Ey+F=0#

We calculate the discriminant #Delta=B^2-4AC#

Here, we have

#x^2+y^2-2x+6y+9=0#

#Delta=0-4*1*1=-4#

#Delta<0#, so we have a circle, center #(1,-3)# and radius #=1#

#x^2-2x+y^2+6y=-9#

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

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

graph{x^2+y^2-2x+6y+9=0 [-5.2, 4.662, -4.088, 0.845]}