Question 1015227
Let {{{Ax^2 +Bxy +Cy^2 + Dx + Ey +F = 0}}} be the general form of the equation of a conic section in cartesian coordinates.  
Then 

if {{{B^2 - 4AC > 0}}}, the conic section is a hyperbola;
if {{{B^2 - 4AC =0}}}, the conic section is a parabola;
if {{{B^2 - 4AC < 0}}}, the conic section is a ellipse.
The given equation equation can be rewritten as
 
{{{x^2 -3y^2 +16y-36 = 0}}} in general form

Since for the given equation  {{{B^2 - 4AC = 0 - 4(1)(-3) = 12>0}}}, the conic section is a hyperbola.  The equation does NOT represent a circle.