Question 697821
It should have a term with {{{x^2}}}.
If {{{x^2+y^2+kxy+8x-6y+9=0}}} represents a circle,
{{{k=0}}}.
(Terms in {{{xy}}} appear when a conic section other than a circle has axes that are not parallel to the x- and y-axes, but circles do not care about rotating the axes).
 
{{{x^2+y^2+8x-6y+9=0}}} --> {{{(x^2+8x)+(y^2-6y)=-9}}} --> {{{(x^2+8x+16)+(y^2-6y+9)=-9+16+9}}} --> {{{(x+4)^2+(x-3)^2=16}}} --> {{{(x+4)^2+(x-3)^2=4^2}}}
The last equation shows that the circle is centered at the point (-4,3),
because {{{x[C]=-4}}} and {{{y[C]=3}}} are the coordinates of the center, subtracted from {{{x}}} and {{{y}}} in the equation.
It also shows that the radius is {{{4}}}.