Definitnost

q[x_,y_]:=9x^2-6x y+y^2
q[1,3]

a0=1;
sl1=ContourPlot[q[x,y]==a0,{x,-5,5},{y,-5,5}];
sl2=Plot3D[q[x,y],{x,-5,5},{y,-5,5}];
GraphicsGrid[{{sl1,sl2}}]

Krivulje drugog reda

a=3; b=2;
ContourPlot[x^2/a^2+y^2/b^2==1,{x,-2a,2a},{y,-2b,2b}, AspectRatio->Automatic]

P[x_,y_]:=2x^2+2x y +2y^2+4x+8y-1
sl1=ContourPlot[P[x,y]==0,{x,-5,5},{y,-5,5}];
sl2=Plot3D[P[x,y],{x,-5,5},{y,-5,5}];
GraphicsGrid[{{sl1,sl2}}]

(* Kruznica radijusa 2*)
slk=ContourPlot[x^2+y^2==2^2,{x,-2,2},{y,-2,2},
Axes->True,Frame->False];
(* Elipsa s poluosima a=3, b=2 *)
sle=ContourPlot[x^2/3^2+y^2/2^2==1,{x,-3,3},{y,-2,2},
AspectRatio->Automatic,Axes->True,Frame->False];
(* Hiperbola s poluosima a=b=1 *)
slh=ContourPlot[x^2-y^2==1,{x,-3,3},{y,-2,2},
AspectRatio->Automatic,Axes->True,Frame->False];
(* Parabola s parametrom p=1 *)
slp=ContourPlot[y^2==2x,{x,-3,3},{y,-2,2},
AspectRatio->Automatic,Axes->True,Frame->False];
Print[GraphicsGrid[{{slk,sle},{slh,slp}}]]