{"id":1438,"date":"2023-06-05T14:51:44","date_gmt":"2023-06-05T14:51:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-the-hyperbola\/"},"modified":"2023-06-05T14:51:44","modified_gmt":"2023-06-05T14:51:44","slug":"solutions-for-the-hyperbola","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-the-hyperbola\/","title":{"raw":"Solutions 66: The Hyperbola","rendered":"Solutions 66: The Hyperbola"},"content":{"raw":"\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n1.&nbsp;A hyperbola is the set of points in a plane the difference of whose distances from two fixed points (foci) is a positive constant.\n\n3.&nbsp;The foci must lie on the transverse axis and be in the interior of the hyperbola.\n\n5.&nbsp;The center must be the midpoint of the line segment joining the foci.\n\n7.&nbsp;yes [latex]\\frac{{x}^{2}}{{6}^{2}}-\\frac{{y}^{2}}{{3}^{2}}=1[\/latex]\n\n9.&nbsp;yes [latex]\\frac{{x}^{2}}{{4}^{2}}-\\frac{{y}^{2}}{{5}^{2}}=1[\/latex]\n\n11.&nbsp;[latex]\\frac{{x}^{2}}{{5}^{2}}-\\frac{{y}^{2}}{{6}^{2}}=1[\/latex]; vertices: [latex]\\left(5,0\\right),\\left(-5,0\\right)[\/latex]; foci: [latex]\\left(\\sqrt{61},0\\right),\\left(-\\sqrt{61},0\\right)[\/latex]; asymptotes: [latex]y=\\frac{6}{5}x,y=-\\frac{6}{5}x[\/latex]\n\n13.&nbsp;[latex]\\frac{{y}^{2}}{{2}^{2}}-\\frac{{x}^{2}}{{9}^{2}}=1[\/latex]; vertices: [latex]\\left(0,2\\right),\\left(0,-2\\right)[\/latex]; foci: [latex]\\left(0,\\sqrt{85}\\right),\\left(0,-\\sqrt{85}\\right)[\/latex]; asymptotes: [latex]y=\\frac{2}{9}x,y=-\\frac{2}{9}x[\/latex]\n\n15.&nbsp;[latex]\\frac{{\\left(x - 1\\right)}^{2}}{{3}^{2}}-\\frac{{\\left(y - 2\\right)}^{2}}{{4}^{2}}=1[\/latex]; vertices: [latex]\\left(4,2\\right),\\left(-2,2\\right)[\/latex]; foci: [latex]\\left(6,2\\right),\\left(-4,2\\right)[\/latex]; asymptotes: [latex]y=\\frac{4}{3}\\left(x - 1\\right)+2,y=-\\frac{4}{3}\\left(x - 1\\right)+2[\/latex]\n\n17.&nbsp;[latex]\\frac{{\\left(x - 2\\right)}^{2}}{{7}^{2}}-\\frac{{\\left(y+7\\right)}^{2}}{{7}^{2}}=1[\/latex]; vertices: [latex]\\left(9,-7\\right),\\left(-5,-7\\right)[\/latex]; foci: [latex]\\left(2+7\\sqrt{2},-7\\right),\\left(2 - 7\\sqrt{2},-7\\right)[\/latex]; asymptotes: [latex]y=x - 9,y=-x - 5[\/latex]\n\n19.&nbsp;[latex]\\frac{{\\left(x+3\\right)}^{2}}{{3}^{2}}-\\frac{{\\left(y - 3\\right)}^{2}}{{3}^{2}}=1[\/latex]; vertices: [latex]\\left(0,3\\right),\\left(-6,3\\right)[\/latex]; foci: [latex]\\left(-3+3\\sqrt{2},1\\right),\\left(-3 - 3\\sqrt{2},1\\right)[\/latex]; asymptotes: [latex]y=x+6,y=-x[\/latex]\n\n21.&nbsp;[latex]\\frac{{\\left(y - 4\\right)}^{2}}{{2}^{2}}-\\frac{{\\left(x - 3\\right)}^{2}}{{4}^{2}}=1[\/latex]; vertices: [latex]\\left(3,6\\right),\\left(3,2\\right)[\/latex]; foci: [latex]\\left(3,4+2\\sqrt{5}\\right),\\left(3,4 - 2\\sqrt{5}\\right)[\/latex]; asymptotes: [latex]y=\\frac{1}{2}\\left(x - 3\\right)+4,y=-\\frac{1}{2}\\left(x - 3\\right)+4[\/latex]\n\n23.&nbsp;[latex]\\frac{{\\left(y+5\\right)}^{2}}{{7}^{2}}-\\frac{{\\left(x+1\\right)}^{2}}{{70}^{2}}=1[\/latex]; vertices: [latex]\\left(-1,2\\right),\\left(-1,-12\\right)[\/latex]; foci: [latex]\\left(-1,-5+7\\sqrt{101}\\right),\\left(-1,-5 - 7\\sqrt{101}\\right)[\/latex]; asymptotes: [latex]y=\\frac{1}{10}\\left(x+1\\right)-5,y=-\\frac{1}{10}\\left(x+1\\right)-5[\/latex]\n\n25.&nbsp;[latex]\\frac{{\\left(x+3\\right)}^{2}}{{5}^{2}}-\\frac{{\\left(y - 4\\right)}^{2}}{{2}^{2}}=1[\/latex]; vertices: [latex]\\left(2,4\\right),\\left(-8,4\\right)[\/latex]; foci: [latex]\\left(-3+\\sqrt{29},4\\right),\\left(-3-\\sqrt{29},4\\right)[\/latex]; asymptotes: [latex]y=\\frac{2}{5}\\left(x+3\\right)+4,y=-\\frac{2}{5}\\left(x+3\\right)+4[\/latex]\n\n27.&nbsp;[latex]y=\\frac{2}{5}\\left(x - 3\\right)-4,y=-\\frac{2}{5}\\left(x - 3\\right)-4[\/latex]\n\n29.&nbsp;[latex]y=\\frac{3}{4}\\left(x - 1\\right)+1,y=-\\frac{3}{4}\\left(x - 1\\right)+1[\/latex]\n\n31.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182848\/CNX_Precalc_Figure_10_02_201.jpg\" alt=\"\">\n\n33.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182850\/CNX_Precalc_Figure_10_02_203.jpg\" alt=\"\">\n\n35.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182852\/CNX_Precalc_Figure_10_02_205.jpg\" alt=\"\">\n\n37.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182855\/CNX_Precalc_Figure_10_02_207.jpg\" alt=\"\">\n\n39.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182857\/CNX_Precalc_Figure_10_02_209.jpg\" alt=\"\">\n\n41.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182859\/CNX_Precalc_Figure_10_02_211.jpg\" alt=\"\">\n\n43.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182901\/CNX_Precalc_Figure_10_02_213.jpg\" alt=\"\">\n\n45.&nbsp;[latex]\\frac{{x}^{2}}{9}-\\frac{{y}^{2}}{16}=1[\/latex]\n\n47.&nbsp;[latex]\\frac{{\\left(x - 6\\right)}^{2}}{25}-\\frac{{\\left(y - 1\\right)}^{2}}{11}=1[\/latex]\n\n49.&nbsp;[latex]\\frac{{\\left(x - 4\\right)}^{2}}{25}-\\frac{{\\left(y - 2\\right)}^{2}}{1}=1[\/latex]\n\n51.&nbsp;[latex]\\frac{{y}^{2}}{16}-\\frac{{x}^{2}}{25}=1[\/latex]\n\n53.&nbsp;[latex]\\frac{{y}^{2}}{9}-\\frac{{\\left(x+1\\right)}^{2}}{9}=1[\/latex]\n\n55.&nbsp;[latex]\\frac{{\\left(x+3\\right)}^{2}}{25}-\\frac{{\\left(y+3\\right)}^{2}}{25}=1[\/latex]\n\n57.&nbsp;[latex]y\\left(x\\right)=3\\sqrt{{x}^{2}+1},y\\left(x\\right)=-3\\sqrt{{x}^{2}+1}[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182904\/CNX_Precalc_Figure_10_02_226.jpg\" alt=\"\">\n\n59.&nbsp;[latex]y\\left(x\\right)=1+2\\sqrt{{x}^{2}+4x+5},y\\left(x\\right)=1 - 2\\sqrt{{x}^{2}+4x+5}[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182906\/CNX_Precalc_Figure_10_02_228.jpg\" alt=\"\">\n\n61.&nbsp;[latex]\\frac{{x}^{2}}{25}-\\frac{{y}^{2}}{25}=1[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182908\/CNX_Precalc_Figure_10_02_220.jpg\" alt=\"\">\n\n63.&nbsp;[latex]\\frac{{x}^{2}}{100}-\\frac{{y}^{2}}{25}=1[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182910\/CNX_Precalc_Figure_10_02_222.jpg\" alt=\"\">\n\n65.&nbsp;[latex]\\frac{{x}^{2}}{400}-\\frac{{y}^{2}}{225}=1[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182912\/CNX_Precalc_Figure_10_02_224.jpg\" alt=\"\">\n\n67.&nbsp;[latex]\\frac{{\\left(x - 1\\right)}^{2}}{0.25}-\\frac{{y}^{2}}{0.75}=1[\/latex]\n\n69.&nbsp;[latex]\\frac{{\\left(x - 3\\right)}^{2}}{4}-\\frac{{y}^{2}}{5}=1[\/latex]\n","rendered":"<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.&nbsp;A hyperbola is the set of points in a plane the difference of whose distances from two fixed points (foci) is a positive constant.<\/p>\n<p>3.&nbsp;The foci must lie on the transverse axis and be in the interior of the hyperbola.<\/p>\n<p>5.&nbsp;The center must be the midpoint of the line segment joining the foci.<\/p>\n<p>7.&nbsp;yes [latex]\\frac{{x}^{2}}{{6}^{2}}-\\frac{{y}^{2}}{{3}^{2}}=1[\/latex]<\/p>\n<p>9.&nbsp;yes [latex]\\frac{{x}^{2}}{{4}^{2}}-\\frac{{y}^{2}}{{5}^{2}}=1[\/latex]<\/p>\n<p>11.&nbsp;[latex]\\frac{{x}^{2}}{{5}^{2}}-\\frac{{y}^{2}}{{6}^{2}}=1[\/latex]; vertices: [latex]\\left(5,0\\right),\\left(-5,0\\right)[\/latex]; foci: [latex]\\left(\\sqrt{61},0\\right),\\left(-\\sqrt{61},0\\right)[\/latex]; asymptotes: [latex]y=\\frac{6}{5}x,y=-\\frac{6}{5}x[\/latex]<\/p>\n<p>13.&nbsp;[latex]\\frac{{y}^{2}}{{2}^{2}}-\\frac{{x}^{2}}{{9}^{2}}=1[\/latex]; vertices: [latex]\\left(0,2\\right),\\left(0,-2\\right)[\/latex]; foci: [latex]\\left(0,\\sqrt{85}\\right),\\left(0,-\\sqrt{85}\\right)[\/latex]; asymptotes: [latex]y=\\frac{2}{9}x,y=-\\frac{2}{9}x[\/latex]<\/p>\n<p>15.&nbsp;[latex]\\frac{{\\left(x - 1\\right)}^{2}}{{3}^{2}}-\\frac{{\\left(y - 2\\right)}^{2}}{{4}^{2}}=1[\/latex]; vertices: [latex]\\left(4,2\\right),\\left(-2,2\\right)[\/latex]; foci: [latex]\\left(6,2\\right),\\left(-4,2\\right)[\/latex]; asymptotes: [latex]y=\\frac{4}{3}\\left(x - 1\\right)+2,y=-\\frac{4}{3}\\left(x - 1\\right)+2[\/latex]<\/p>\n<p>17.&nbsp;[latex]\\frac{{\\left(x - 2\\right)}^{2}}{{7}^{2}}-\\frac{{\\left(y+7\\right)}^{2}}{{7}^{2}}=1[\/latex]; vertices: [latex]\\left(9,-7\\right),\\left(-5,-7\\right)[\/latex]; foci: [latex]\\left(2+7\\sqrt{2},-7\\right),\\left(2 - 7\\sqrt{2},-7\\right)[\/latex]; asymptotes: [latex]y=x - 9,y=-x - 5[\/latex]<\/p>\n<p>19.&nbsp;[latex]\\frac{{\\left(x+3\\right)}^{2}}{{3}^{2}}-\\frac{{\\left(y - 3\\right)}^{2}}{{3}^{2}}=1[\/latex]; vertices: [latex]\\left(0,3\\right),\\left(-6,3\\right)[\/latex]; foci: [latex]\\left(-3+3\\sqrt{2},1\\right),\\left(-3 - 3\\sqrt{2},1\\right)[\/latex]; asymptotes: [latex]y=x+6,y=-x[\/latex]<\/p>\n<p>21.&nbsp;[latex]\\frac{{\\left(y - 4\\right)}^{2}}{{2}^{2}}-\\frac{{\\left(x - 3\\right)}^{2}}{{4}^{2}}=1[\/latex]; vertices: [latex]\\left(3,6\\right),\\left(3,2\\right)[\/latex]; foci: [latex]\\left(3,4+2\\sqrt{5}\\right),\\left(3,4 - 2\\sqrt{5}\\right)[\/latex]; asymptotes: [latex]y=\\frac{1}{2}\\left(x - 3\\right)+4,y=-\\frac{1}{2}\\left(x - 3\\right)+4[\/latex]<\/p>\n<p>23.&nbsp;[latex]\\frac{{\\left(y+5\\right)}^{2}}{{7}^{2}}-\\frac{{\\left(x+1\\right)}^{2}}{{70}^{2}}=1[\/latex]; vertices: [latex]\\left(-1,2\\right),\\left(-1,-12\\right)[\/latex]; foci: [latex]\\left(-1,-5+7\\sqrt{101}\\right),\\left(-1,-5 - 7\\sqrt{101}\\right)[\/latex]; asymptotes: [latex]y=\\frac{1}{10}\\left(x+1\\right)-5,y=-\\frac{1}{10}\\left(x+1\\right)-5[\/latex]<\/p>\n<p>25.&nbsp;[latex]\\frac{{\\left(x+3\\right)}^{2}}{{5}^{2}}-\\frac{{\\left(y - 4\\right)}^{2}}{{2}^{2}}=1[\/latex]; vertices: [latex]\\left(2,4\\right),\\left(-8,4\\right)[\/latex]; foci: [latex]\\left(-3+\\sqrt{29},4\\right),\\left(-3-\\sqrt{29},4\\right)[\/latex]; asymptotes: [latex]y=\\frac{2}{5}\\left(x+3\\right)+4,y=-\\frac{2}{5}\\left(x+3\\right)+4[\/latex]<\/p>\n<p>27.&nbsp;[latex]y=\\frac{2}{5}\\left(x - 3\\right)-4,y=-\\frac{2}{5}\\left(x - 3\\right)-4[\/latex]<\/p>\n<p>29.&nbsp;[latex]y=\\frac{3}{4}\\left(x - 1\\right)+1,y=-\\frac{3}{4}\\left(x - 1\\right)+1[\/latex]<\/p>\n<p>31.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182848\/CNX_Precalc_Figure_10_02_201.jpg\" alt=\"\" \/><\/p>\n<p>33.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182850\/CNX_Precalc_Figure_10_02_203.jpg\" alt=\"\" \/><\/p>\n<p>35.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182852\/CNX_Precalc_Figure_10_02_205.jpg\" alt=\"\" \/><\/p>\n<p>37.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182855\/CNX_Precalc_Figure_10_02_207.jpg\" alt=\"\" \/><\/p>\n<p>39.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182857\/CNX_Precalc_Figure_10_02_209.jpg\" alt=\"\" \/><\/p>\n<p>41.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182859\/CNX_Precalc_Figure_10_02_211.jpg\" alt=\"\" \/><\/p>\n<p>43.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182901\/CNX_Precalc_Figure_10_02_213.jpg\" alt=\"\" \/><\/p>\n<p>45.&nbsp;[latex]\\frac{{x}^{2}}{9}-\\frac{{y}^{2}}{16}=1[\/latex]<\/p>\n<p>47.&nbsp;[latex]\\frac{{\\left(x - 6\\right)}^{2}}{25}-\\frac{{\\left(y - 1\\right)}^{2}}{11}=1[\/latex]<\/p>\n<p>49.&nbsp;[latex]\\frac{{\\left(x - 4\\right)}^{2}}{25}-\\frac{{\\left(y - 2\\right)}^{2}}{1}=1[\/latex]<\/p>\n<p>51.&nbsp;[latex]\\frac{{y}^{2}}{16}-\\frac{{x}^{2}}{25}=1[\/latex]<\/p>\n<p>53.&nbsp;[latex]\\frac{{y}^{2}}{9}-\\frac{{\\left(x+1\\right)}^{2}}{9}=1[\/latex]<\/p>\n<p>55.&nbsp;[latex]\\frac{{\\left(x+3\\right)}^{2}}{25}-\\frac{{\\left(y+3\\right)}^{2}}{25}=1[\/latex]<\/p>\n<p>57.&nbsp;[latex]y\\left(x\\right)=3\\sqrt{{x}^{2}+1},y\\left(x\\right)=-3\\sqrt{{x}^{2}+1}[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182904\/CNX_Precalc_Figure_10_02_226.jpg\" alt=\"\" \/><\/p>\n<p>59.&nbsp;[latex]y\\left(x\\right)=1+2\\sqrt{{x}^{2}+4x+5},y\\left(x\\right)=1 - 2\\sqrt{{x}^{2}+4x+5}[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182906\/CNX_Precalc_Figure_10_02_228.jpg\" alt=\"\" \/><\/p>\n<p>61.&nbsp;[latex]\\frac{{x}^{2}}{25}-\\frac{{y}^{2}}{25}=1[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182908\/CNX_Precalc_Figure_10_02_220.jpg\" alt=\"\" \/><\/p>\n<p>63.&nbsp;[latex]\\frac{{x}^{2}}{100}-\\frac{{y}^{2}}{25}=1[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182910\/CNX_Precalc_Figure_10_02_222.jpg\" alt=\"\" \/><\/p>\n<p>65.&nbsp;[latex]\\frac{{x}^{2}}{400}-\\frac{{y}^{2}}{225}=1[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27182912\/CNX_Precalc_Figure_10_02_224.jpg\" alt=\"\" \/><\/p>\n<p>67.&nbsp;[latex]\\frac{{\\left(x - 1\\right)}^{2}}{0.25}-\\frac{{y}^{2}}{0.75}=1[\/latex]<\/p>\n<p>69.&nbsp;[latex]\\frac{{\\left(x - 3\\right)}^{2}}{4}-\\frac{{y}^{2}}{5}=1[\/latex]<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1438\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":503070,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1438","chapter","type-chapter","status-publish","hentry"],"part":1429,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/users\/503070"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1438\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/parts\/1429"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1438\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/media?parent=1438"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapter-type?post=1438"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/contributor?post=1438"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/license?post=1438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}