{"id":1440,"date":"2023-06-05T14:51:45","date_gmt":"2023-06-05T14:51:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-the-parabola\/"},"modified":"2023-06-05T14:51:45","modified_gmt":"2023-06-05T14:51:45","slug":"solutions-for-the-parabola","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-the-parabola\/","title":{"raw":"Solutions 67: The Parabola","rendered":"Solutions 67: The Parabola"},"content":{"raw":"\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n1.&nbsp;A parabola is the set of points in the plane that lie equidistant from a fixed point, the focus, and a fixed line, the directrix.\n\n3.&nbsp;The graph will open down.\n\n5.&nbsp;The distance between the focus and directrix will increase.\n\n7.&nbsp;yes [latex]y=4\\left(1\\right){x}^{2}[\/latex]\n\n9.&nbsp;yes [latex]{\\left(y - 3\\right)}^{2}=4\\left(2\\right)\\left(x - 2\\right)[\/latex]\n\n11.&nbsp;[latex]{y}^{2}=\\frac{1}{8}x,V:\\left(0,0\\right);F:\\left(\\frac{1}{32},0\\right);d:x=-\\frac{1}{32}[\/latex]\n\n13.&nbsp;[latex]{x}^{2}=-\\frac{1}{4}y,V:\\left(0,0\\right);F:\\left(0,-\\frac{1}{16}\\right);d:y=\\frac{1}{16}[\/latex]\n\n15.&nbsp;[latex]{y}^{2}=\\frac{1}{36}x,V:\\left(0,0\\right);F:\\left(\\frac{1}{144},0\\right);d:x=-\\frac{1}{144}[\/latex]\n\n17.&nbsp;[latex]{\\left(x - 1\\right)}^{2}=4\\left(y - 1\\right),V:\\left(1,1\\right);F:\\left(1,2\\right);d:y=0[\/latex]\n\n19.&nbsp;[latex]{\\left(y - 4\\right)}^{2}=2\\left(x+3\\right),V:\\left(-3,4\\right);F:\\left(-\\frac{5}{2},4\\right);d:x=-\\frac{7}{2}[\/latex]\n\n21.&nbsp;[latex]{\\left(x+4\\right)}^{2}=24\\left(y+1\\right),V:\\left(-4,-1\\right);F:\\left(-4,5\\right);d:y=-7[\/latex]\n\n23.&nbsp;[latex]{\\left(y - 3\\right)}^{2}=-12\\left(x+1\\right),V:\\left(-1,3\\right);F:\\left(-4,3\\right);d:x=2[\/latex]\n\n25.&nbsp;[latex]{\\left(x - 5\\right)}^{2}=\\frac{4}{5}\\left(y+3\\right),V:\\left(5,-3\\right);F:\\left(5,-\\frac{14}{5}\\right);d:y=-\\frac{16}{5}[\/latex]\n\n27.&nbsp;[latex]{\\left(x - 2\\right)}^{2}=-2\\left(y - 5\\right),V:\\left(2,5\\right);F:\\left(2,\\frac{9}{2}\\right);d:y=\\frac{11}{2}[\/latex]\n\n29.&nbsp;[latex]{\\left(y - 1\\right)}^{2}=\\frac{4}{3}\\left(x - 5\\right),V:\\left(5,1\\right);F:\\left(\\frac{16}{3},1\\right);d:x=\\frac{14}{3}[\/latex]\n\n31.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183005\/CNX_Precalc_Figure_10_03_2012.jpg\" alt=\"\">\n\n33.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183007\/CNX_Precalc_Figure_10_03_2032.jpg\" alt=\"\">\n\n35.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183010\/CNX_Precalc_Figure_10_03_2052.jpg\" alt=\"\">\n\n37.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183012\/CNX_Precalc_Figure_10_03_2072.jpg\" alt=\"\">\n\n39.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183014\/CNX_Precalc_Figure_10_03_2092.jpg\" alt=\"\">\n\n41.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183016\/CNX_Precalc_Figure_10_03_2112.jpg\" alt=\"\">\n\n43.\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27183019\/CNX_Precalc_Figure_10_03_2132.jpg\" alt=\"\">\n\n45.&nbsp;[latex]{x}^{2}=-16y[\/latex]\n\n47.&nbsp;[latex]{\\left(y - 2\\right)}^{2}=4\\sqrt{2}\\left(x - 2\\right)[\/latex]\n\n49.&nbsp;[latex]{\\left(y+\\sqrt{3}\\right)}^{2}=-4\\sqrt{2}\\left(x-\\sqrt{2}\\right)[\/latex]\n\n51.&nbsp;[latex]{x}^{2}=y[\/latex]\n\n53.&nbsp;[latex]{\\left(y - 2\\right)}^{2}=\\frac{1}{4}\\left(x+2\\right)[\/latex]\n\n55.&nbsp;[latex]{\\left(y-\\sqrt{3}\\right)}^{2}=4\\sqrt{5}\\left(x+\\sqrt{2}\\right)[\/latex]\n\n57.&nbsp;[latex]{y}^{2}=-8x[\/latex]\n\n59.&nbsp;[latex]{\\left(y+1\\right)}^{2}=12\\left(x+3\\right)[\/latex]\n\n61.&nbsp;[latex]\\left(0,1\\right)[\/latex]\n\n63.&nbsp;At the point 2.25 feet above the vertex.\n\n65.&nbsp;0.5625 feet\n\n67.&nbsp;[latex]{x}^{2}=-125\\left(y - 20\\right)[\/latex],&nbsp;height is 7.2 feet\n\n69.&nbsp;2304 feet\n","rendered":"<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.&nbsp;A parabola is the set of points in the plane that lie equidistant from a fixed point, the focus, and a fixed line, the directrix.<\/p>\n<p>3.&nbsp;The graph will open down.<\/p>\n<p>5.&nbsp;The distance between the focus and directrix will increase.<\/p>\n<p>7.&nbsp;yes [latex]y=4\\left(1\\right){x}^{2}[\/latex]<\/p>\n<p>9.&nbsp;yes [latex]{\\left(y - 3\\right)}^{2}=4\\left(2\\right)\\left(x - 2\\right)[\/latex]<\/p>\n<p>11.&nbsp;[latex]{y}^{2}=\\frac{1}{8}x,V:\\left(0,0\\right);F:\\left(\\frac{1}{32},0\\right);d:x=-\\frac{1}{32}[\/latex]<\/p>\n<p>13.&nbsp;[latex]{x}^{2}=-\\frac{1}{4}y,V:\\left(0,0\\right);F:\\left(0,-\\frac{1}{16}\\right);d:y=\\frac{1}{16}[\/latex]<\/p>\n<p>15.&nbsp;[latex]{y}^{2}=\\frac{1}{36}x,V:\\left(0,0\\right);F:\\left(\\frac{1}{144},0\\right);d:x=-\\frac{1}{144}[\/latex]<\/p>\n<p>17.&nbsp;[latex]{\\left(x - 1\\right)}^{2}=4\\left(y - 1\\right),V:\\left(1,1\\right);F:\\left(1,2\\right);d:y=0[\/latex]<\/p>\n<p>19.&nbsp;[latex]{\\left(y - 4\\right)}^{2}=2\\left(x+3\\right),V:\\left(-3,4\\right);F:\\left(-\\frac{5}{2},4\\right);d:x=-\\frac{7}{2}[\/latex]<\/p>\n<p>21.&nbsp;[latex]{\\left(x+4\\right)}^{2}=24\\left(y+1\\right),V:\\left(-4,-1\\right);F:\\left(-4,5\\right);d:y=-7[\/latex]<\/p>\n<p>23.&nbsp;[latex]{\\left(y - 3\\right)}^{2}=-12\\left(x+1\\right),V:\\left(-1,3\\right);F:\\left(-4,3\\right);d:x=2[\/latex]<\/p>\n<p>25.&nbsp;[latex]{\\left(x - 5\\right)}^{2}=\\frac{4}{5}\\left(y+3\\right),V:\\left(5,-3\\right);F:\\left(5,-\\frac{14}{5}\\right);d:y=-\\frac{16}{5}[\/latex]<\/p>\n<p>27.&nbsp;[latex]{\\left(x - 2\\right)}^{2}=-2\\left(y - 5\\right),V:\\left(2,5\\right);F:\\left(2,\\frac{9}{2}\\right);d:y=\\frac{11}{2}[\/latex]<\/p>\n<p>29.&nbsp;[latex]{\\left(y - 1\\right)}^{2}=\\frac{4}{3}\\left(x - 5\\right),V:\\left(5,1\\right);F:\\left(\\frac{16}{3},1\\right);d:x=\\frac{14}{3}[\/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\/27183005\/CNX_Precalc_Figure_10_03_2012.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\/27183007\/CNX_Precalc_Figure_10_03_2032.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\/27183010\/CNX_Precalc_Figure_10_03_2052.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\/27183012\/CNX_Precalc_Figure_10_03_2072.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\/27183014\/CNX_Precalc_Figure_10_03_2092.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\/27183016\/CNX_Precalc_Figure_10_03_2112.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\/27183019\/CNX_Precalc_Figure_10_03_2132.jpg\" alt=\"\" \/><\/p>\n<p>45.&nbsp;[latex]{x}^{2}=-16y[\/latex]<\/p>\n<p>47.&nbsp;[latex]{\\left(y - 2\\right)}^{2}=4\\sqrt{2}\\left(x - 2\\right)[\/latex]<\/p>\n<p>49.&nbsp;[latex]{\\left(y+\\sqrt{3}\\right)}^{2}=-4\\sqrt{2}\\left(x-\\sqrt{2}\\right)[\/latex]<\/p>\n<p>51.&nbsp;[latex]{x}^{2}=y[\/latex]<\/p>\n<p>53.&nbsp;[latex]{\\left(y - 2\\right)}^{2}=\\frac{1}{4}\\left(x+2\\right)[\/latex]<\/p>\n<p>55.&nbsp;[latex]{\\left(y-\\sqrt{3}\\right)}^{2}=4\\sqrt{5}\\left(x+\\sqrt{2}\\right)[\/latex]<\/p>\n<p>57.&nbsp;[latex]{y}^{2}=-8x[\/latex]<\/p>\n<p>59.&nbsp;[latex]{\\left(y+1\\right)}^{2}=12\\left(x+3\\right)[\/latex]<\/p>\n<p>61.&nbsp;[latex]\\left(0,1\\right)[\/latex]<\/p>\n<p>63.&nbsp;At the point 2.25 feet above the vertex.<\/p>\n<p>65.&nbsp;0.5625 feet<\/p>\n<p>67.&nbsp;[latex]{x}^{2}=-125\\left(y - 20\\right)[\/latex],&nbsp;height is 7.2 feet<\/p>\n<p>69.&nbsp;2304 feet<\/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-1440\">\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":11,"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-1440","chapter","type-chapter","status-publish","hentry"],"part":1429,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1440","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\/1440\/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\/1440\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/media?parent=1440"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapter-type?post=1440"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/contributor?post=1440"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/license?post=1440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}