{"id":1999,"date":"2015-11-12T18:30:43","date_gmt":"2015-11-12T18:30:43","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=1999"},"modified":"2015-11-12T18:30:43","modified_gmt":"2015-11-12T18:30:43","slug":"solutions-16","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-16\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\n1. ellipse; [latex]e=\\frac{1}{3};x=-2[\/latex]\n\n2.\n\"\"\n\n3.\u00a0[latex]r=\\frac{1}{1-\\cos \\theta }[\/latex]\n\n4.\u00a0[latex]4 - 8x+3{x}^{2}-{y}^{2}=0[\/latex]\n

Solutions to Odd-Numbered Exercises<\/h2>\n1.\u00a0If eccentricity is less than 1, it is an ellipse. If eccentricity is equal to 1, it is a parabola. If eccentricity is greater than 1, it is a hyperbola.\n\n3.\u00a0The directrix will be parallel to the polar axis.\n\n5.\u00a0One of the foci will be located at the origin.\n\n7.\u00a0Parabola with [latex]e=1[\/latex] and directrix [latex]\\frac{3}{4}[\/latex] units below the pole.\n\n9.\u00a0Hyperbola with [latex]e=2[\/latex] and directrix [latex]\\frac{5}{2}[\/latex] units above the pole.\n\n11.\u00a0Parabola with [latex]e=1[\/latex] and directrix [latex]\\frac{3}{10}[\/latex] units to the right of the pole.\n\n13.\u00a0Ellipse with [latex]e=\\frac{2}{7}[\/latex] and directrix [latex]2[\/latex] units to the right of the pole.\n\n15.\u00a0Hyperbola with [latex]e=\\frac{5}{3}[\/latex] and directrix [latex]\\frac{11}{5}[\/latex] units above the pole.\n\n17.\u00a0Hyperbola with [latex]e=\\frac{8}{7}[\/latex] and directrix [latex]\\frac{7}{8}[\/latex] units to the right of the pole.\n\n19.\u00a0[latex]25{x}^{2}+16{y}^{2}-12y - 4=0[\/latex]\n\n21.\u00a0[latex]21{x}^{2}-4{y}^{2}-30x+9=0[\/latex]\n\n23.\u00a0[latex]64{y}^{2}=48x+9[\/latex]\n\n25.\u00a0[latex]96{y}^{2}-25{x}^{2}+110y+25=0[\/latex]\n\n27.\u00a0[latex]3{x}^{2}+4{y}^{2}-2x - 1=0[\/latex]\n\n29.\u00a0[latex]5{x}^{2}+9{y}^{2}-24x - 36=0[\/latex]\n\n31.\n\"\"\n\n33.\n\"\"\n\n35.\n\"\"\n\n37.\n\"\"\n\n39.\n\"\"\n\n41.\n\"\"\n\n43.\u00a0[latex]r=\\frac{4}{5+\\cos \\theta }[\/latex]\n\n45.\u00a0[latex]r=\\frac{4}{1+2\\sin \\theta }[\/latex]\n\n47.\u00a0[latex]r=\\frac{1}{1+\\cos \\theta }[\/latex]\n\n49.\u00a0[latex]r=\\frac{7}{8 - 28\\cos \\theta }[\/latex]\n\n51.\u00a0[latex]r=\\frac{12}{2+3\\sin \\theta }[\/latex]\n\n53.\u00a0[latex]r=\\frac{15}{4 - 3\\cos \\theta }[\/latex]\n\n55.\u00a0[latex]r=\\frac{3}{3 - 3\\cos \\theta }[\/latex]\n\n57.\u00a0[latex]r=\\pm \\frac{2}{\\sqrt{1+\\sin \\theta \\cos \\theta }}[\/latex]\n\n59.\u00a0[latex]r=\\pm \\frac{2}{4\\cos \\theta +3\\sin \\theta }[\/latex]","rendered":"

Solutions to Try Its<\/h2>\n

1. ellipse; [latex]e=\\frac{1}{3};x=-2[\/latex]<\/p>\n

2.
\n\"\"<\/p>\n

3.\u00a0[latex]r=\\frac{1}{1-\\cos \\theta }[\/latex]<\/p>\n

4.\u00a0[latex]4 - 8x+3{x}^{2}-{y}^{2}=0[\/latex]<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0If eccentricity is less than 1, it is an ellipse. If eccentricity is equal to 1, it is a parabola. If eccentricity is greater than 1, it is a hyperbola.<\/p>\n

3.\u00a0The directrix will be parallel to the polar axis.<\/p>\n

5.\u00a0One of the foci will be located at the origin.<\/p>\n

7.\u00a0Parabola with [latex]e=1[\/latex] and directrix [latex]\\frac{3}{4}[\/latex] units below the pole.<\/p>\n

9.\u00a0Hyperbola with [latex]e=2[\/latex] and directrix [latex]\\frac{5}{2}[\/latex] units above the pole.<\/p>\n

11.\u00a0Parabola with [latex]e=1[\/latex] and directrix [latex]\\frac{3}{10}[\/latex] units to the right of the pole.<\/p>\n

13.\u00a0Ellipse with [latex]e=\\frac{2}{7}[\/latex] and directrix [latex]2[\/latex] units to the right of the pole.<\/p>\n

15.\u00a0Hyperbola with [latex]e=\\frac{5}{3}[\/latex] and directrix [latex]\\frac{11}{5}[\/latex] units above the pole.<\/p>\n

17.\u00a0Hyperbola with [latex]e=\\frac{8}{7}[\/latex] and directrix [latex]\\frac{7}{8}[\/latex] units to the right of the pole.<\/p>\n

19.\u00a0[latex]25{x}^{2}+16{y}^{2}-12y - 4=0[\/latex]<\/p>\n

21.\u00a0[latex]21{x}^{2}-4{y}^{2}-30x+9=0[\/latex]<\/p>\n

23.\u00a0[latex]64{y}^{2}=48x+9[\/latex]<\/p>\n

25.\u00a0[latex]96{y}^{2}-25{x}^{2}+110y+25=0[\/latex]<\/p>\n

27.\u00a0[latex]3{x}^{2}+4{y}^{2}-2x - 1=0[\/latex]<\/p>\n

29.\u00a0[latex]5{x}^{2}+9{y}^{2}-24x - 36=0[\/latex]<\/p>\n

31.
\n\"\"<\/p>\n

33.
\n\"\"<\/p>\n

35.
\n\"\"<\/p>\n

37.
\n\"\"<\/p>\n

39.
\n\"\"<\/p>\n

41.
\n\"\"<\/p>\n

43.\u00a0[latex]r=\\frac{4}{5+\\cos \\theta }[\/latex]<\/p>\n

45.\u00a0[latex]r=\\frac{4}{1+2\\sin \\theta }[\/latex]<\/p>\n

47.\u00a0[latex]r=\\frac{1}{1+\\cos \\theta }[\/latex]<\/p>\n

49.\u00a0[latex]r=\\frac{7}{8 - 28\\cos \\theta }[\/latex]<\/p>\n

51.\u00a0[latex]r=\\frac{12}{2+3\\sin \\theta }[\/latex]<\/p>\n

53.\u00a0[latex]r=\\frac{15}{4 - 3\\cos \\theta }[\/latex]<\/p>\n

55.\u00a0[latex]r=\\frac{3}{3 - 3\\cos \\theta }[\/latex]<\/p>\n

57.\u00a0[latex]r=\\pm \\frac{2}{\\sqrt{1+\\sin \\theta \\cos \\theta }}[\/latex]<\/p>\n

59.\u00a0[latex]r=\\pm \\frac{2}{4\\cos \\theta +3\\sin \\theta }[\/latex]<\/p>\n\n\t\t\t

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