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# 12.4E: Rotation of Axes (Exercises)

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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. $$6 x^{2}+24 x y-y^{2}-12 x+26 y+11=0$$

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