General Form of the Equation
Key Questions

The general form of a circle looks like ...
#x^2+y^2+Ax+By+C=0# In the standard form to the equation for a circle look like ...
#(xh)^2+(yk)^2=r^2# #sqrt(r^2)=r,# radiusConvert the general form to standard form by using the completing the square process.
You will then have the
#r^2# value.The square root of
#r^2# is the radius of the circle. 
General equation of ellipse or circle
#(xh)^2/a^2+(yk)^2/b^2=1# If
#a=b# then you have a circle.If
#a>b# then you have an ellipse where the#x# axis is the major axis.If
#b>a# then you have an ellipse where the#y# axis is the major axis. 
Answer:
A circle in general form has the same nonzero coefficients for the
#x^2# and the#y^2# terms. So if there is a graph, it is a circle (or a point).Explanation:
Don't be too hasty, though.
#Ax^2+Bxy+Cy^2+Dx+Ey+F=0# Assuming that there is ineed a graph, it is:
an ellipse if
#A# and#C# have the same sign.a circle if
#A=C# .However it is possible that there is no graph:
#x^2+y^2=9/4# Has no graph, but it can be rewritten as:#4x^2+4y^2+9=0# . At first look, this appears to be the equation of a circle, but it is not.