Here's a start on solution to your problem. Equation should probably read
36 x^2 - 24 x y + 29 y^2 + 72 x - 354 y + 945 = 0
Discriminant D = B^2 - 4 A C
In[16]:= (-24)^2 - 4*36*29
Out[16]= -3600
D < 0 so you have an ellipse
Now plot equation
In[22]:= Solve[36 x^2 - 24 x y + 29 y^2 + 72 x - 354 y + 945 == 0, y]
Out[22]= {{y -> 3/29 (59 + 4 x - 2 Sqrt[109 + 60 x - 25 x^2])}, {y ->
3/29 (59 + 4 x + 2 Sqrt[109 + 60 x - 25 x^2])}}
In[23]:= Plot[{3/29 (59 + 4 x - 2 Sqrt[109 + 60 x - 25 x^2]),
3/29 (59 + 4 x + 2 Sqrt[109 + 60 x - 25 x^2])}, {x, -10, 10},
PlotRange -> All]
Can't show output.
To put into standard form, complete the squares for x and y terms. Then you can figure out the angle of rotation.
