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Mathematics LibreTexts

12.4E: Rotation of Axes (Exercises)

  • Page ID
    56134
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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. \(6 x^{2}+24 x y-y^{2}-12 x+26 y+11=0\)


    12.4E: Rotation of Axes (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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