12.4E: Rotation of Axes (Exercises)
For the following exercises, determine which of the conic sections is represented.
33. \(16 x^{2}+24 x y+9 y^{2}+24 x-60 y-60=0\)
34. \(4 x^{2}+14 x y+5 y^{2}+18 x-6 y+30=0\)
35. \(4 x^{2}+x y+2 y^{2}+8 x-26 y+9=0\)
For the following exercises, determine the angle \(\theta\) that will eliminate the \(x y\) term, and write the corresponding equation without the \(x y\) term.
36. \(x^{2}+4 x y-2 y^{2}-6=0\)
37. \(x^{2}-x y+y^{2}-6=0\)
For the following exercises, graph the equation relative to the \(x^{\prime} y^{\prime}\) system in which the equation has no \(x^{\prime} y^{\prime}\) term.
38. \(9 x^{2}-24 x y+16 y^{2}-80 x-60 y+100=0\)
39. \(x^{2}-x y+y^{2}-2=0\)
40. \(6 x^{2}+24 x y-y^{2}-12 x+26 y+11=0\)