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

1 Answer
Nov 30, 2016

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

Explanation:

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]}