{"id":186,"date":"2026-01-12T16:01:11","date_gmt":"2026-01-12T16:01:11","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=186"},"modified":"2026-01-12T16:01:12","modified_gmt":"2026-01-12T16:01:12","slug":"polar-coordinates-and-conic-sections-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/polar-coordinates-and-conic-sections-get-stronger-answer-key\/","title":{"raw":"Polar Coordinates and Conic Sections: Get Stronger Answer Key","rendered":"Polar Coordinates and Conic Sections: Get Stronger Answer Key"},"content":{"raw":"

Understanding Polar Coordinates<\/span><\/h2>\r\n
    \r\n \t
  1. \"On<\/li>\r\n \t
  2. \"On<\/li>\r\n \t
  3. \"On<\/li>\r\n \t
  4. \"On<\/li>\r\n \t
  5. [latex]B\\begin{array}{cc}\\left(3,\\dfrac{\\text{-}\\pi }{3}\\right)\\hfill & B\\left(-3,\\dfrac{2\\pi }{3}\\right)\\hfill \\end{array}[\/latex]<\/li>\r\n \t
  6. [latex]D\\left(5,\\dfrac{7\\pi }{6}\\right)D\\left(-5,\\dfrac{\\pi }{6}\\right)[\/latex]<\/li>\r\n \t
  7. [latex]\\begin{array}{cc}\\left(5,-0.927\\right)\\hfill & \\left(-5,-0.927+\\pi \\right)\\hfill \\end{array}[\/latex]<\/li>\r\n \t
  8. [latex]\\left(10,-0.927\\right)\\left(-10,-0.927+\\pi \\right)[\/latex]<\/li>\r\n \t
  9. [latex]\\left(2\\sqrt{3},-0.524\\right)\\left(-2\\sqrt{3},-0.524+\\pi \\right)[\/latex]<\/li>\r\n \t
  10. [latex]\\left(\\begin{array}{cc}\\text{-}\\sqrt{3},\\hfill & -1\\hfill \\end{array}\\right)[\/latex]<\/li>\r\n \t
  11. [latex]\\left(\\begin{array}{cc}-\\dfrac{\\sqrt{3}}{2},\\hfill & \\dfrac{-1}{2}\\hfill \\end{array}\\right)[\/latex]<\/li>\r\n \t
  12. [latex]\\left(\\begin{array}{cc}0,\\hfill & 0\\hfill \\end{array}\\right)[\/latex]<\/li>\r\n \t
  13. Symmetry with respect to the [latex]x[\/latex]-axis, [latex]y[\/latex]-axis, and origin.<\/li>\r\n \t
  14. Symmetric with respect to [latex]x[\/latex]-axis only.<\/li>\r\n \t
  15. Symmetry with respect to [latex]x[\/latex]-axis only.<\/li>\r\n \t
  16. Line [latex]y=x[\/latex]<\/li>\r\n \t
  17. [latex]y=1[\/latex]<\/li>\r\n \t
  18. \"A\r\nHyperbola; polar form [latex]{r}^{2}\\cos\\left(2\\theta \\right)=16[\/latex] or [latex]{r}^{2}=16\\sec\\theta [\/latex].<\/li>\r\n \t
  19. \"A\r\n[latex]r=\\dfrac{2}{3\\cos\\theta -\\sin\\theta }[\/latex]<\/li>\r\n \t
  20. \"A\r\n[latex]{x}^{2}+{y}^{2}=4y[\/latex]<\/li>\r\n \t
  21. \"A\r\n[latex]x\\tan\\sqrt{{x}^{2}+{y}^{2}}=y[\/latex]<\/li>\r\n \t
  22. \"A\r\n[latex]y[\/latex]-axis symmetry<\/li>\r\n \t
  23. \"A\r\n[latex]y[\/latex]-axis symmetry<\/li>\r\n \t
  24. \"A\r\n[latex]x[\/latex]- and [latex]y[\/latex]-axis symmetry and symmetry about the pole<\/li>\r\n \t
  25. \"A\r\n[latex]x[\/latex]-axis symmetry<\/li>\r\n \t
  26. \"The\r\n[latex]x[\/latex]- and [latex]y[\/latex]-axis symmetry and symmetry about the pole<\/li>\r\n \t
  27. \"A\r\nno symmetry<\/li>\r\n<\/ol>\r\n

    Area and Arc Length in Polar Coordinates<\/span><\/h2>\r\n
      \r\n \t
    1. [latex]\\dfrac{9}{2}{\\displaystyle\\int }_{0}^{\\pi }{\\sin}^{2}\\theta d\\theta [\/latex]<\/li>\r\n \t
    2. [latex]32{\\displaystyle\\int }_{0}^{\\frac{\\pi}{2}}{\\sin}^{2}\\left(2\\theta \\right)d\\theta [\/latex]<\/li>\r\n \t
    3. [latex]\\dfrac{1}{2}{\\displaystyle\\int }_{\\pi }^{2\\pi }{\\left(1-\\sin\\theta \\right)}^{2}d\\theta [\/latex]<\/li>\r\n \t
    4. [latex]{\\displaystyle\\int }_{{\\sin}^{-1}\\left(\\frac{2}{3}\\right)}^{\\frac{\\pi}{2}}{\\left(2 - 3\\sin\\theta \\right)}^{2}d\\theta [\/latex]<\/li>\r\n \t
    5. [latex]{\\displaystyle\\int }{0}^{\\pi }{\\left(1 - 2\\cos\\theta \\right)}^{2}d\\theta -{\\displaystyle\\int }{0}^{\\frac{\\pi}{3}}{\\left(1 - 2\\cos\\theta \\right)}^{2}d\\theta [\/latex]<\/li>\r\n \t
    6. [latex]4{\\displaystyle\\int }{0}^{\\frac{\\pi}{3}}d\\theta +16{\\displaystyle\\int }{\\frac{\\pi}{3}}^{\\frac{\\pi}{2}}\\left({\\cos}^{2}\\theta \\right)d\\theta [\/latex]<\/li>\r\n \t
    7. [latex]9\\pi [\/latex]<\/li>\r\n \t
    8. [latex]\\dfrac{9\\pi }{4}[\/latex]<\/li>\r\n \t
    9. [latex]\\dfrac{9\\pi }{8}[\/latex]<\/li>\r\n \t
    10. [latex]\\dfrac{18\\pi -27\\sqrt{3}}{2}[\/latex]<\/li>\r\n \t
    11. [latex]\\dfrac{4}{3}\\left(4\\pi -3\\sqrt{3}\\right)[\/latex]<\/li>\r\n \t
    12. [latex]\\dfrac{3}{2}\\left(4\\pi -3\\sqrt{3}\\right)[\/latex]<\/li>\r\n \t
    13. [latex]2\\pi -4[\/latex]<\/li>\r\n \t
    14. [latex]{\\displaystyle\\int }_{0}^{2\\pi }\\sqrt{{\\left(1+\\sin\\theta \\right)}^{2}+{\\cos}^{2}\\theta }d\\theta [\/latex]<\/li>\r\n \t
    15. [latex]\\sqrt{2}{\\displaystyle\\int }_{0}^{1}{e}^{\\theta }d\\theta [\/latex]<\/li>\r\n \t
    16. [latex]\\dfrac{\\sqrt{10}}{3}\\left({e}^{6}-1\\right)[\/latex]<\/li>\r\n \t
    17. [latex]32[\/latex]<\/li>\r\n \t
    18. [latex]6.238[\/latex]<\/li>\r\n \t
    19. [latex]2[\/latex]<\/li>\r\n \t
    20. [latex]4.39[\/latex]<\/li>\r\n \t
    21. [latex]A=\\pi {\\left(\\dfrac{\\sqrt{2}}{2}\\right)}^{2}=\\dfrac{\\pi }{2}\\text{ and }\\dfrac{1}{2}{\\displaystyle\\int }_{0}^{\\pi }\\left(1+2\\sin\\theta \\cos\\theta \\right)d\\theta =\\dfrac{\\pi }{2}[\/latex]<\/li>\r\n \t
    22. [latex]C=2\\pi \\left(\\dfrac{3}{2}\\right)=3\\pi \\text{ and }{\\displaystyle\\int }_{0}^{\\pi }3d\\theta =3\\pi [\/latex]<\/li>\r\n \t
    23. [latex]C=2\\pi \\left(5\\right)=10\\pi \\text{ and }{\\displaystyle\\int }_{0}^{\\pi }10d\\theta =10\\pi [\/latex]<\/li>\r\n \t
    24. [latex]\\dfrac{dy}{dx}=\\dfrac{{f}^{\\prime }\\left(\\theta \\right)\\sin\\theta +f\\left(\\theta \\right)\\cos\\theta }{{f}^{\\prime }\\left(\\theta \\right)\\cos\\theta -f\\left(\\theta \\right)\\sin\\theta }[\/latex]<\/li>\r\n \t
    25. The slope is [latex]\\dfrac{1}{\\sqrt{3}}[\/latex].<\/li>\r\n \t
    26. The slope is [latex]0[\/latex].<\/li>\r\n \t
    27. At [latex]\\left(4,0\\right)[\/latex], the slope is undefined. At [latex]\\left(-4,\\dfrac{\\pi }{2}\\right)[\/latex], the slope is 0.<\/li>\r\n \t
    28. The slope is undefined at [latex]\\theta =\\dfrac{\\pi }{4}[\/latex].<\/li>\r\n \t
    29. Slope =[latex] \u22121[\/latex].<\/li>\r\n \t
    30. Slope is [latex]\\dfrac{-2}{\\pi }[\/latex].<\/li>\r\n \t
    31. Calculator answer: [latex]\u22120.836.[\/latex]<\/li>\r\n \t
    32. Horizontal tangent at [latex]\\left(\\pm\\sqrt{2},\\dfrac{\\pi }{6}\\right)[\/latex], [latex]\\left(\\pm\\sqrt{2},-\\dfrac{\\pi }{6}\\right)[\/latex].<\/li>\r\n \t
    33. Horizontal tangents at [latex]\\dfrac{\\pi }{2},\\dfrac{7\\pi }{6},\\dfrac{11\\pi }{6}[\/latex]. Vertical tangents at [latex]\\dfrac{\\pi }{6},\\dfrac{5\\pi }{6}[\/latex] and also at the pole [latex]\\left(0,0\\right)[\/latex].<\/li>\r\n<\/ol>\r\n

      Conic Sections<\/span><\/h2>\r\n
        \r\n \t
      1. [latex]{y}^{2}=16x[\/latex]<\/li>\r\n \t
      2. [latex]{x}^{2}=2y[\/latex]<\/li>\r\n \t
      3. [latex]{x}^{2}=-4\\left(y - 3\\right)[\/latex]<\/li>\r\n \t
      4. [latex]{\\left(x+3\\right)}^{2}=8\\left(y - 3\\right)[\/latex]<\/li>\r\n \t
      5. [latex]\\dfrac{{x}^{2}}{16}+\\dfrac{{y}^{2}}{12}=1[\/latex]<\/li>\r\n \t
      6. [latex]\\dfrac{{x}^{2}}{13}+\\dfrac{{y}^{2}}{4}=1[\/latex]<\/li>\r\n \t
      7. [latex]\\dfrac{{\\left(y - 1\\right)}^{2}}{16}+\\dfrac{{\\left(x+3\\right)}^{2}}{12}=1[\/latex]<\/li>\r\n \t
      8. [latex]\\dfrac{{x}^{2}}{16}+\\dfrac{{y}^{2}}{12}=1[\/latex]<\/li>\r\n \t
      9. [latex]\\dfrac{{x}^{2}}{25}-\\dfrac{{y}^{2}}{11}=1[\/latex]<\/li>\r\n \t
      10. [latex]\\dfrac{{x}^{2}}{7}-\\dfrac{{y}^{2}}{9}=1[\/latex]<\/li>\r\n \t
      11. [latex]\\dfrac{{\\left(y+2\\right)}^{2}}{4}-\\dfrac{{\\left(x+2\\right)}^{2}}{32}=1[\/latex]<\/li>\r\n \t
      12. [latex]\\dfrac{{x}^{2}}{4}-\\dfrac{{y}^{2}}{32}=1[\/latex]<\/li>\r\n \t
      13. [latex]e=1[\/latex], parabola<\/li>\r\n \t
      14. [latex]e=\\dfrac{1}{2}[\/latex], ellipse<\/li>\r\n \t
      15. [latex]e=3[\/latex], hyperbola<\/li>\r\n \t
      16. [latex]r=\\dfrac{4}{5+\\cos\\theta }[\/latex]<\/li>\r\n \t
      17. [latex]r=\\dfrac{4}{1+2\\sin\\theta }[\/latex]<\/li>\r\n \t
      18. Hyperbola<\/li>\r\n \t
      19. Ellipse<\/li>\r\n \t
      20. Ellipse<\/li>\r\n<\/ol>","rendered":"

        Understanding Polar Coordinates<\/span><\/h2>\n
          \n
        1. \"On<\/li>\n
        2. \"On<\/li>\n
        3. \"On<\/li>\n
        4. \"On<\/li>\n
        5. [latex]B\\begin{array}{cc}\\left(3,\\dfrac{\\text{-}\\pi }{3}\\right)\\hfill & B\\left(-3,\\dfrac{2\\pi }{3}\\right)\\hfill \\end{array}[\/latex]<\/li>\n
        6. [latex]D\\left(5,\\dfrac{7\\pi }{6}\\right)D\\left(-5,\\dfrac{\\pi }{6}\\right)[\/latex]<\/li>\n
        7. [latex]\\begin{array}{cc}\\left(5,-0.927\\right)\\hfill & \\left(-5,-0.927+\\pi \\right)\\hfill \\end{array}[\/latex]<\/li>\n
        8. [latex]\\left(10,-0.927\\right)\\left(-10,-0.927+\\pi \\right)[\/latex]<\/li>\n
        9. [latex]\\left(2\\sqrt{3},-0.524\\right)\\left(-2\\sqrt{3},-0.524+\\pi \\right)[\/latex]<\/li>\n
        10. [latex]\\left(\\begin{array}{cc}\\text{-}\\sqrt{3},\\hfill & -1\\hfill \\end{array}\\right)[\/latex]<\/li>\n
        11. [latex]\\left(\\begin{array}{cc}-\\dfrac{\\sqrt{3}}{2},\\hfill & \\dfrac{-1}{2}\\hfill \\end{array}\\right)[\/latex]<\/li>\n
        12. [latex]\\left(\\begin{array}{cc}0,\\hfill & 0\\hfill \\end{array}\\right)[\/latex]<\/li>\n
        13. Symmetry with respect to the [latex]x[\/latex]-axis, [latex]y[\/latex]-axis, and origin.<\/li>\n
        14. Symmetric with respect to [latex]x[\/latex]-axis only.<\/li>\n
        15. Symmetry with respect to [latex]x[\/latex]-axis only.<\/li>\n
        16. Line [latex]y=x[\/latex]<\/li>\n
        17. [latex]y=1[\/latex]<\/li>\n
        18. \"A
          \nHyperbola; polar form [latex]{r}^{2}\\cos\\left(2\\theta \\right)=16[\/latex] or [latex]{r}^{2}=16\\sec\\theta[\/latex].<\/li>\n
        19. \"A
          \n[latex]r=\\dfrac{2}{3\\cos\\theta -\\sin\\theta }[\/latex]<\/li>\n
        20. \"A
          \n[latex]{x}^{2}+{y}^{2}=4y[\/latex]<\/li>\n
        21. \"A
          \n[latex]x\\tan\\sqrt{{x}^{2}+{y}^{2}}=y[\/latex]<\/li>\n
        22. \"A
          \n[latex]y[\/latex]-axis symmetry<\/li>\n
        23. \"A
          \n[latex]y[\/latex]-axis symmetry<\/li>\n
        24. \"A
          \n[latex]x[\/latex]– and [latex]y[\/latex]-axis symmetry and symmetry about the pole<\/li>\n
        25. \"A
          \n[latex]x[\/latex]-axis symmetry<\/li>\n
        26. \"The
          \n[latex]x[\/latex]– and [latex]y[\/latex]-axis symmetry and symmetry about the pole<\/li>\n
        27. \"A
          \nno symmetry<\/li>\n<\/ol>\n

          Area and Arc Length in Polar Coordinates<\/span><\/h2>\n
            \n
          1. [latex]\\dfrac{9}{2}{\\displaystyle\\int }_{0}^{\\pi }{\\sin}^{2}\\theta d\\theta[\/latex]<\/li>\n
          2. [latex]32{\\displaystyle\\int }_{0}^{\\frac{\\pi}{2}}{\\sin}^{2}\\left(2\\theta \\right)d\\theta[\/latex]<\/li>\n
          3. [latex]\\dfrac{1}{2}{\\displaystyle\\int }_{\\pi }^{2\\pi }{\\left(1-\\sin\\theta \\right)}^{2}d\\theta[\/latex]<\/li>\n
          4. [latex]{\\displaystyle\\int }_{{\\sin}^{-1}\\left(\\frac{2}{3}\\right)}^{\\frac{\\pi}{2}}{\\left(2 - 3\\sin\\theta \\right)}^{2}d\\theta[\/latex]<\/li>\n
          5. [latex]{\\displaystyle\\int }{0}^{\\pi }{\\left(1 - 2\\cos\\theta \\right)}^{2}d\\theta -{\\displaystyle\\int }{0}^{\\frac{\\pi}{3}}{\\left(1 - 2\\cos\\theta \\right)}^{2}d\\theta[\/latex]<\/li>\n
          6. [latex]4{\\displaystyle\\int }{0}^{\\frac{\\pi}{3}}d\\theta +16{\\displaystyle\\int }{\\frac{\\pi}{3}}^{\\frac{\\pi}{2}}\\left({\\cos}^{2}\\theta \\right)d\\theta[\/latex]<\/li>\n
          7. [latex]9\\pi[\/latex]<\/li>\n
          8. [latex]\\dfrac{9\\pi }{4}[\/latex]<\/li>\n
          9. [latex]\\dfrac{9\\pi }{8}[\/latex]<\/li>\n
          10. [latex]\\dfrac{18\\pi -27\\sqrt{3}}{2}[\/latex]<\/li>\n
          11. [latex]\\dfrac{4}{3}\\left(4\\pi -3\\sqrt{3}\\right)[\/latex]<\/li>\n
          12. [latex]\\dfrac{3}{2}\\left(4\\pi -3\\sqrt{3}\\right)[\/latex]<\/li>\n
          13. [latex]2\\pi -4[\/latex]<\/li>\n
          14. [latex]{\\displaystyle\\int }_{0}^{2\\pi }\\sqrt{{\\left(1+\\sin\\theta \\right)}^{2}+{\\cos}^{2}\\theta }d\\theta[\/latex]<\/li>\n
          15. [latex]\\sqrt{2}{\\displaystyle\\int }_{0}^{1}{e}^{\\theta }d\\theta[\/latex]<\/li>\n
          16. [latex]\\dfrac{\\sqrt{10}}{3}\\left({e}^{6}-1\\right)[\/latex]<\/li>\n
          17. [latex]32[\/latex]<\/li>\n
          18. [latex]6.238[\/latex]<\/li>\n
          19. [latex]2[\/latex]<\/li>\n
          20. [latex]4.39[\/latex]<\/li>\n
          21. [latex]A=\\pi {\\left(\\dfrac{\\sqrt{2}}{2}\\right)}^{2}=\\dfrac{\\pi }{2}\\text{ and }\\dfrac{1}{2}{\\displaystyle\\int }_{0}^{\\pi }\\left(1+2\\sin\\theta \\cos\\theta \\right)d\\theta =\\dfrac{\\pi }{2}[\/latex]<\/li>\n
          22. [latex]C=2\\pi \\left(\\dfrac{3}{2}\\right)=3\\pi \\text{ and }{\\displaystyle\\int }_{0}^{\\pi }3d\\theta =3\\pi[\/latex]<\/li>\n
          23. [latex]C=2\\pi \\left(5\\right)=10\\pi \\text{ and }{\\displaystyle\\int }_{0}^{\\pi }10d\\theta =10\\pi[\/latex]<\/li>\n
          24. [latex]\\dfrac{dy}{dx}=\\dfrac{{f}^{\\prime }\\left(\\theta \\right)\\sin\\theta +f\\left(\\theta \\right)\\cos\\theta }{{f}^{\\prime }\\left(\\theta \\right)\\cos\\theta -f\\left(\\theta \\right)\\sin\\theta }[\/latex]<\/li>\n
          25. The slope is [latex]\\dfrac{1}{\\sqrt{3}}[\/latex].<\/li>\n
          26. The slope is [latex]0[\/latex].<\/li>\n
          27. At [latex]\\left(4,0\\right)[\/latex], the slope is undefined. At [latex]\\left(-4,\\dfrac{\\pi }{2}\\right)[\/latex], the slope is 0.<\/li>\n
          28. The slope is undefined at [latex]\\theta =\\dfrac{\\pi }{4}[\/latex].<\/li>\n
          29. Slope =[latex]\u22121[\/latex].<\/li>\n
          30. Slope is [latex]\\dfrac{-2}{\\pi }[\/latex].<\/li>\n
          31. Calculator answer: [latex]\u22120.836.[\/latex]<\/li>\n
          32. Horizontal tangent at [latex]\\left(\\pm\\sqrt{2},\\dfrac{\\pi }{6}\\right)[\/latex], [latex]\\left(\\pm\\sqrt{2},-\\dfrac{\\pi }{6}\\right)[\/latex].<\/li>\n
          33. Horizontal tangents at [latex]\\dfrac{\\pi }{2},\\dfrac{7\\pi }{6},\\dfrac{11\\pi }{6}[\/latex]. Vertical tangents at [latex]\\dfrac{\\pi }{6},\\dfrac{5\\pi }{6}[\/latex] and also at the pole [latex]\\left(0,0\\right)[\/latex].<\/li>\n<\/ol>\n

            Conic Sections<\/span><\/h2>\n
              \n
            1. [latex]{y}^{2}=16x[\/latex]<\/li>\n
            2. [latex]{x}^{2}=2y[\/latex]<\/li>\n
            3. [latex]{x}^{2}=-4\\left(y - 3\\right)[\/latex]<\/li>\n
            4. [latex]{\\left(x+3\\right)}^{2}=8\\left(y - 3\\right)[\/latex]<\/li>\n
            5. [latex]\\dfrac{{x}^{2}}{16}+\\dfrac{{y}^{2}}{12}=1[\/latex]<\/li>\n
            6. [latex]\\dfrac{{x}^{2}}{13}+\\dfrac{{y}^{2}}{4}=1[\/latex]<\/li>\n
            7. [latex]\\dfrac{{\\left(y - 1\\right)}^{2}}{16}+\\dfrac{{\\left(x+3\\right)}^{2}}{12}=1[\/latex]<\/li>\n
            8. [latex]\\dfrac{{x}^{2}}{16}+\\dfrac{{y}^{2}}{12}=1[\/latex]<\/li>\n
            9. [latex]\\dfrac{{x}^{2}}{25}-\\dfrac{{y}^{2}}{11}=1[\/latex]<\/li>\n
            10. [latex]\\dfrac{{x}^{2}}{7}-\\dfrac{{y}^{2}}{9}=1[\/latex]<\/li>\n
            11. [latex]\\dfrac{{\\left(y+2\\right)}^{2}}{4}-\\dfrac{{\\left(x+2\\right)}^{2}}{32}=1[\/latex]<\/li>\n
            12. [latex]\\dfrac{{x}^{2}}{4}-\\dfrac{{y}^{2}}{32}=1[\/latex]<\/li>\n
            13. [latex]e=1[\/latex], parabola<\/li>\n
            14. [latex]e=\\dfrac{1}{2}[\/latex], ellipse<\/li>\n
            15. [latex]e=3[\/latex], hyperbola<\/li>\n
            16. [latex]r=\\dfrac{4}{5+\\cos\\theta }[\/latex]<\/li>\n
            17. [latex]r=\\dfrac{4}{1+2\\sin\\theta }[\/latex]<\/li>\n
            18. Hyperbola<\/li>\n
            19. Ellipse<\/li>\n
            20. Ellipse<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":109,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/186"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/186\/revisions"}],"predecessor-version":[{"id":197,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/186\/revisions\/197"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/109"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/186\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=186"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=186"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=186"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}