{"id":1977,"date":"2015-11-12T18:30:43","date_gmt":"2015-11-12T18:30:43","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1977"},"modified":"2015-11-12T18:30:43","modified_gmt":"2015-11-12T18:30:43","slug":"solutions-17","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/solutions-17\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"<h2>Solutions to Try Its<\/h2>\n1.\n<ul><li>hyperbola<\/li>\n\t<li>ellipse<\/li>\n<\/ul>\n2.\u00a0[latex]\\frac{{{x}^{\\prime }}^{2}}{4}+\\frac{{{y}^{\\prime }}^{2}}{1}=1[\/latex]\n\n3.\n<ul><li>hyperbola<\/li>\n\t<li>ellipse<\/li>\n<\/ul><h2>Solutions to Odd-Numbered Exercises<\/h2>\n1.\u00a0The [latex]xy[\/latex] term causes a rotation of the graph to occur.\n\n3.\u00a0The conic section is a hyperbola.\n\n5.\u00a0It gives the angle of rotation of the axes in order to eliminate the [latex]xy[\/latex] term.\n\n7.\u00a0[latex]AB=0[\/latex], parabola\n\n9.\u00a0[latex]AB=-4&lt;0[\/latex], hyperbola\n\n11.\u00a0[latex]AB=6&gt;0[\/latex], ellipse\n\n13.\u00a0[latex]{B}^{2}-4AC=0[\/latex], parabola\n\n15.\u00a0[latex]{B}^{2}-4AC=0[\/latex], parabola\n\n17.\u00a0[latex]{B}^{2}-4AC=-96&lt;0[\/latex], ellipse\n\n19.\u00a0[latex]7{{x}^{\\prime }}^{2}+9{{y}^{\\prime }}^{2}-4=0[\/latex]\n\n21.\u00a0[latex]3{{x}^{\\prime }}^{2}+2{x}^{\\prime }{y}^{\\prime }-5{{y}^{\\prime }}^{2}+1=0[\/latex]\n\n23.\u00a0[latex]\\theta ={60}^{\\circ },11{{x}^{\\prime }}^{2}-{{y}^{\\prime }}^{2}+\\sqrt{3}{x}^{\\prime }+{y}^{\\prime }-4=0[\/latex]\n\n25.\u00a0[latex]\\theta ={150}^{\\circ },21{{x}^{\\prime }}^{2}+9{{y}^{\\prime }}^{2}+4{x}^{\\prime }-4\\sqrt{3}{y}^{\\prime }-6=0[\/latex]\n\n27.\u00a0[latex]\\theta \\approx {36.9}^{\\circ },125{{x}^{\\prime }}^{2}+6{x}^{\\prime }-42{y}^{\\prime }+10=0[\/latex]\n\n29.\u00a0[latex]\\theta ={45}^{\\circ },3{{x}^{\\prime }}^{2}-{{y}^{\\prime }}^{2}-\\sqrt{2}{x}^{\\prime }+\\sqrt{2}{y}^{\\prime }+1=0[\/latex]\n\n31.\u00a0[latex]\\frac{\\sqrt{2}}{2}\\left({x}^{\\prime }+{y}^{\\prime }\\right)=\\frac{1}{2}{\\left({x}^{\\prime }-{y}^{\\prime }\\right)}^{2}[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202415\/CNX_Precalc_Figure_10_04_2012.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n33.\u00a0[latex]\\frac{{\\left({x}^{\\prime }-{y}^{\\prime }\\right)}^{2}}{8}+\\frac{{\\left({x}^{\\prime }+{y}^{\\prime }\\right)}^{2}}{2}=1[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202416\/CNX_Precalc_Figure_10_04_2032.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n35.\u00a0[latex]\\frac{{\\left({x}^{\\prime }+{y}^{\\prime }\\right)}^{2}}{2}-\\frac{{\\left({x}^{\\prime }-{y}^{\\prime }\\right)}^{2}}{2}=1[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202417\/CNX_Precalc_Figure_10_04_2052.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n37.\u00a0[latex]\\frac{\\sqrt{3}}{2}{x}^{\\prime }-\\frac{1}{2}{y}^{\\prime }={\\left(\\frac{1}{2}{x}^{\\prime }+\\frac{\\sqrt{3}}{2}{y}^{\\prime }-1\\right)}^{2}[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202419\/CNX_Precalc_Figure_10_04_2072.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n39.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202420\/CNX_Precalc_Figure_10_04_2092.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n41.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202421\/CNX_Precalc_Figure_10_04_2112.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n43.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202423\/CNX_Precalc_Figure_10_04_2132.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n45.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202424\/CNX_Precalc_Figure_10_04_2152.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n47.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202426\/CNX_Precalc_Figure_10_04_217.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n49.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202427\/CNX_Precalc_Figure_10_04_219.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n51.\u00a0[latex]\\theta ={45}^{\\circ }[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202428\/CNX_Precalc_Figure_10_04_221.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n53.\u00a0[latex]\\theta ={60}^{\\circ }[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202430\/CNX_Precalc_Figure_10_04_223.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n55.\u00a0[latex]\\theta \\approx {36.9}^{\\circ }[\/latex]\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202432\/CNX_Precalc_Figure_10_04_225.jpg\" alt=\"\" data-media-type=\"image\/jpg\"\/>\n\n57. [latex]-4\\sqrt{6}&lt;k&lt;4\\sqrt{6}[\/latex]\n\n59.\u00a0[latex]k=2[\/latex]","rendered":"<h2>Solutions to Try Its<\/h2>\n<p>1.<\/p>\n<ul>\n<li>hyperbola<\/li>\n<li>ellipse<\/li>\n<\/ul>\n<p>2.\u00a0[latex]\\frac{{{x}^{\\prime }}^{2}}{4}+\\frac{{{y}^{\\prime }}^{2}}{1}=1[\/latex]<\/p>\n<p>3.<\/p>\n<ul>\n<li>hyperbola<\/li>\n<li>ellipse<\/li>\n<\/ul>\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.\u00a0The [latex]xy[\/latex] term causes a rotation of the graph to occur.<\/p>\n<p>3.\u00a0The conic section is a hyperbola.<\/p>\n<p>5.\u00a0It gives the angle of rotation of the axes in order to eliminate the [latex]xy[\/latex] term.<\/p>\n<p>7.\u00a0[latex]AB=0[\/latex], parabola<\/p>\n<p>9.\u00a0[latex]AB=-4<0[\/latex], hyperbola\n\n11.\u00a0[latex]AB=6>0[\/latex], ellipse<\/p>\n<p>13.\u00a0[latex]{B}^{2}-4AC=0[\/latex], parabola<\/p>\n<p>15.\u00a0[latex]{B}^{2}-4AC=0[\/latex], parabola<\/p>\n<p>17.\u00a0[latex]{B}^{2}-4AC=-96<0[\/latex], ellipse\n\n19.\u00a0[latex]7{{x}^{\\prime }}^{2}+9{{y}^{\\prime }}^{2}-4=0[\/latex]\n\n21.\u00a0[latex]3{{x}^{\\prime }}^{2}+2{x}^{\\prime }{y}^{\\prime }-5{{y}^{\\prime }}^{2}+1=0[\/latex]\n\n23.\u00a0[latex]\\theta ={60}^{\\circ },11{{x}^{\\prime }}^{2}-{{y}^{\\prime }}^{2}+\\sqrt{3}{x}^{\\prime }+{y}^{\\prime }-4=0[\/latex]\n\n25.\u00a0[latex]\\theta ={150}^{\\circ },21{{x}^{\\prime }}^{2}+9{{y}^{\\prime }}^{2}+4{x}^{\\prime }-4\\sqrt{3}{y}^{\\prime }-6=0[\/latex]\n\n27.\u00a0[latex]\\theta \\approx {36.9}^{\\circ },125{{x}^{\\prime }}^{2}+6{x}^{\\prime }-42{y}^{\\prime }+10=0[\/latex]\n\n29.\u00a0[latex]\\theta ={45}^{\\circ },3{{x}^{\\prime }}^{2}-{{y}^{\\prime }}^{2}-\\sqrt{2}{x}^{\\prime }+\\sqrt{2}{y}^{\\prime }+1=0[\/latex]\n\n31.\u00a0[latex]\\frac{\\sqrt{2}}{2}\\left({x}^{\\prime }+{y}^{\\prime }\\right)=\\frac{1}{2}{\\left({x}^{\\prime }-{y}^{\\prime }\\right)}^{2}[\/latex]\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202415\/CNX_Precalc_Figure_10_04_2012.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>33.\u00a0[latex]\\frac{{\\left({x}^{\\prime }-{y}^{\\prime }\\right)}^{2}}{8}+\\frac{{\\left({x}^{\\prime }+{y}^{\\prime }\\right)}^{2}}{2}=1[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202416\/CNX_Precalc_Figure_10_04_2032.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>35.\u00a0[latex]\\frac{{\\left({x}^{\\prime }+{y}^{\\prime }\\right)}^{2}}{2}-\\frac{{\\left({x}^{\\prime }-{y}^{\\prime }\\right)}^{2}}{2}=1[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202417\/CNX_Precalc_Figure_10_04_2052.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>37.\u00a0[latex]\\frac{\\sqrt{3}}{2}{x}^{\\prime }-\\frac{1}{2}{y}^{\\prime }={\\left(\\frac{1}{2}{x}^{\\prime }+\\frac{\\sqrt{3}}{2}{y}^{\\prime }-1\\right)}^{2}[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202419\/CNX_Precalc_Figure_10_04_2072.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>39.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202420\/CNX_Precalc_Figure_10_04_2092.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>41.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202421\/CNX_Precalc_Figure_10_04_2112.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>43.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202423\/CNX_Precalc_Figure_10_04_2132.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>45.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202424\/CNX_Precalc_Figure_10_04_2152.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>47.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202426\/CNX_Precalc_Figure_10_04_217.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>49.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202427\/CNX_Precalc_Figure_10_04_219.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>51.\u00a0[latex]\\theta ={45}^{\\circ }[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202428\/CNX_Precalc_Figure_10_04_221.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>53.\u00a0[latex]\\theta ={60}^{\\circ }[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202430\/CNX_Precalc_Figure_10_04_223.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>55.\u00a0[latex]\\theta \\approx {36.9}^{\\circ }[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202432\/CNX_Precalc_Figure_10_04_225.jpg\" alt=\"\" data-media-type=\"image\/jpg\" \/><\/p>\n<p>57. [latex]-4\\sqrt{6}<k<4\\sqrt{6}[\/latex]\n\n59.\u00a0[latex]k=2[\/latex]\n<\/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-1977\">\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":276,"menu_order":8,"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-1977","chapter","type-chapter","status-publish","hentry"],"part":1942,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1977","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1977\/revisions"}],"predecessor-version":[{"id":2190,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1977\/revisions\/2190"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1942"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1977\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=1977"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1977"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1977"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=1977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}