You can put this solution on YOUR website! Identify the type of conic and write the equation in standard form:
x^2+y^2-6x+4y+3=0
complete the square
(x^2-6x+9)+(y^2+4y+4)=-3+9+4
(x-3)^2+(y+2)^2=10
This is an equation of a circle with center at (3,-2) and radius of √10