{"id":1862,"date":"2015-11-12T18:30:44","date_gmt":"2015-11-12T18:30:44","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=1862"},"modified":"2015-11-12T18:30:44","modified_gmt":"2015-11-12T18:30:44","slug":"solutions-20","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-20\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\n1.\u00a0[latex]{x}^{2}+\\frac{{y}^{2}}{16}=1[\/latex]\n\n2.\u00a0[latex]\\frac{{\\left(x - 1\\right)}^{2}}{16}+\\frac{{\\left(y - 3\\right)}^{2}}{4}=1[\/latex]\n\n3.\u00a0center: [latex]\\left(0,0\\right)[\/latex]; vertices: [latex]\\left(\\pm 6,0\\right)[\/latex]; co-vertices: [latex]\\left(0,\\pm 2\\right)[\/latex]; foci: [latex]\\left(\\pm 4\\sqrt{2},0\\right)[\/latex]\n\"\"\n\n4.\u00a0Standard form: [latex]\\frac{{x}^{2}}{16}+\\frac{{y}^{2}}{49}=1[\/latex]; center: [latex]\\left(0,0\\right)[\/latex]; vertices: [latex]\\left(0,\\pm 7\\right)[\/latex]; co-vertices: [latex]\\left(\\pm 4,0\\right)[\/latex]; foci: [latex]\\left(0,\\pm \\sqrt{33}\\right)[\/latex]\n\"\"\n\n5.\u00a0Center: [latex]\\left(4,2\\right)[\/latex]; vertices: [latex]\\left(-2,2\\right)[\/latex] and [latex]\\left(10,2\\right)[\/latex]; co-vertices: [latex]\\left(4,2 - 2\\sqrt{5}\\right)[\/latex] and [latex]\\left(4,2+2\\sqrt{5}\\right)[\/latex]; foci: [latex]\\left(0,2\\right)[\/latex] and [latex]\\left(8,2\\right)[\/latex]\n\"\"\n\n6.\u00a0[latex]\\frac{{\\left(x - 3\\right)}^{2}}{4}+\\frac{{\\left(y+1\\right)}^{2}}{16}=1[\/latex]; center: [latex]\\left(3,-1\\right)[\/latex]; vertices: [latex]\\left(3,-\\text{5}\\right)[\/latex] and [latex]\\left(3,\\text{3}\\right)[\/latex]; co-vertices: [latex]\\left(1,-1\\right)[\/latex] and [latex]\\left(5,-1\\right)[\/latex]; foci: [latex]\\left(3,-\\text{1}-2\\sqrt{3}\\right)[\/latex] and [latex]\\left(3,-\\text{1+}2\\sqrt{3}\\right)[\/latex]\n\n7. a.\u00a0[latex]\\frac{{x}^{2}}{57,600}+\\frac{{y}^{2}}{25,600}=1[\/latex]\nb. The people are standing 358 feet apart.\n

Solutions to Odd-Numbered Exercises<\/h2>\n1.\u00a0An ellipse is the set of all points in the plane the sum of whose distances from two fixed points, called the foci, is a constant.\n\n3.\u00a0This special case would be a circle.\n\n5.\u00a0It is symmetric about the x<\/em>-axis, y<\/em>-axis, and the origin.\n\n7.\u00a0yes; [latex]\\frac{{x}^{2}}{{3}^{2}}+\\frac{{y}^{2}}{{2}^{2}}=1[\/latex]\n\n9.\u00a0yes; [latex]\\frac{{x}^{2}}{{\\left(\\frac{1}{2}\\right)}^{2}}+\\frac{{y}^{2}}{{\\left(\\frac{1}{3}\\right)}^{2}}=1[\/latex]\n\n11.\u00a0[latex]\\frac{{x}^{2}}{{2}^{2}}+\\frac{{y}^{2}}{{7}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(0,7\\right)[\/latex] and [latex]\\left(0,-7\\right)[\/latex]. Endpoints of minor axis [latex]\\left(2,0\\right)[\/latex] and [latex]\\left(-2,0\\right)[\/latex]. Foci at [latex]\\left(0,3\\sqrt{5}\\right),\\left(0,-3\\sqrt{5}\\right)[\/latex].\n\n13.\u00a0[latex]\\frac{{x}^{2}}{{\\left(1\\right)}^{2}}+\\frac{{y}^{2}}{{\\left(\\frac{1}{3}\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(1,0\\right)[\/latex] and [latex]\\left(-1,0\\right)[\/latex]. Endpoints of minor axis [latex]\\left(0,\\frac{1}{3}\\right),\\left(0,-\\frac{1}{3}\\right)[\/latex]. Foci at [latex]\\left(\\frac{2\\sqrt{2}}{3},0\\right),\\left(-\\frac{2\\sqrt{2}}{3},0\\right)[\/latex].\n\n15.\u00a0[latex]\\frac{{\\left(x - 2\\right)}^{2}}{{7}^{2}}+\\frac{{\\left(y - 4\\right)}^{2}}{{5}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(9,4\\right),\\left(-5,4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(2,9\\right),\\left(2,-1\\right)[\/latex]. Foci at [latex]\\left(2+2\\sqrt{6},4\\right),\\left(2 - 2\\sqrt{6},4\\right)[\/latex].\n\n17.\u00a0[latex]\\frac{{\\left(x+5\\right)}^{2}}{{2}^{2}}+\\frac{{\\left(y - 7\\right)}^{2}}{{3}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(-5,10\\right),\\left(-5,4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(-3,7\\right),\\left(-7,7\\right)[\/latex]. Foci at [latex]\\left(-5,7+\\sqrt{5}\\right),\\left(-5,7-\\sqrt{5}\\right)[\/latex].\n\n19.\u00a0[latex]\\frac{{\\left(x - 1\\right)}^{2}}{{3}^{2}}+\\frac{{\\left(y - 4\\right)}^{2}}{{2}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(4,4\\right),\\left(-2,4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(1,6\\right),\\left(1,2\\right)[\/latex]. Foci at [latex]\\left(1+\\sqrt{5},4\\right),\\left(1-\\sqrt{5},4\\right)[\/latex].\n\n21.\u00a0[latex]\\frac{{\\left(x - 3\\right)}^{2}}{{\\left(3\\sqrt{2}\\right)}^{2}}+\\frac{{\\left(y - 5\\right)}^{2}}{{\\left(\\sqrt{2}\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(3+3\\sqrt{2},5\\right),\\left(3 - 3\\sqrt{2},5\\right)[\/latex]. Endpoints of minor axis [latex]\\left(3,5+\\sqrt{2}\\right),\\left(3,5-\\sqrt{2}\\right)[\/latex]. Foci at [latex]\\left(7,5\\right),\\left(-1,5\\right)[\/latex].\n\n23.\u00a0[latex]\\frac{{\\left(x+5\\right)}^{2}}{{\\left(5\\right)}^{2}}+\\frac{{\\left(y - 2\\right)}^{2}}{{\\left(2\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(0,2\\right),\\left(-10,2\\right)[\/latex]. Endpoints of minor axis [latex]\\left(-5,4\\right),\\left(-5,0\\right)[\/latex]. Foci at [latex]\\left(-5+\\sqrt{21},2\\right),\\left(-5-\\sqrt{21},2\\right)[\/latex].\n\n25.\u00a0[latex]\\frac{{\\left(x+3\\right)}^{2}}{{\\left(5\\right)}^{2}}+\\frac{{\\left(y+4\\right)}^{2}}{{\\left(2\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(2,-4\\right),\\left(-8,-4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(-3,-2\\right),\\left(-3,-6\\right)[\/latex]. Foci at [latex]\\left(-3+\\sqrt{21},-4\\right),\\left(-3-\\sqrt{21},-4\\right)[\/latex].\n\n27.\u00a0Foci [latex]\\left(-3,-1+\\sqrt{11}\\right),\\left(-3,-1-\\sqrt{11}\\right)[\/latex]\n\n29.\u00a0Focus [latex]\\left(0,0\\right)[\/latex]\n\n31.\u00a0Foci [latex]\\left(-10,30\\right),\\left(-10,-30\\right)[\/latex]\n\n33.\u00a0Center [latex]\\left(0,0\\right)[\/latex], Vertices [latex]\\left(4,0\\right),\\left(-4,0\\right),\\left(0,3\\right),\\left(0,-3\\right)[\/latex], Foci [latex]\\left(\\sqrt{7},0\\right),\\left(-\\sqrt{7},0\\right)[\/latex]\n\"\"\n\n35.\u00a0Center [latex]\\left(0,0\\right)[\/latex], Vertices [latex]\\left(\\frac{1}{9},0\\right),\\left(-\\frac{1}{9},0\\right),\\left(0,\\frac{1}{7}\\right),\\left(0,-\\frac{1}{7}\\right)[\/latex], Foci [latex]\\left(0,\\frac{4\\sqrt{2}}{63}\\right),\\left(0,-\\frac{4\\sqrt{2}}{63}\\right)[\/latex]\n\"\"\n\n37.\u00a0Center [latex]\\left(-3,3\\right)[\/latex], Vertices [latex]\\left(0,3\\right),\\left(-6,3\\right),\\left(-3,0\\right),\\left(-3,6\\right)[\/latex], Focus [latex]\\left(-3,3\\right)[\/latex]\nNote that this ellipse is a circle. The circle has only one focus, which coincides with the center.\n\"\"\n\n39.\u00a0Center [latex]\\left(1,1\\right)[\/latex], Vertices [latex]\\left(5,1\\right),\\left(-3,1\\right),\\left(1,3\\right),\\left(1,-1\\right)[\/latex], Foci [latex]\\left(1,1+4\\sqrt{3}\\right),\\left(1,1 - 4\\sqrt{3}\\right)[\/latex]\n\"\"\n\n41.\u00a0Center [latex]\\left(-4,5\\right)[\/latex], Vertices [latex]\\left(-2,5\\right),\\left(-6,4\\right),\\left(-4,6\\right),\\left(-4,4\\right)[\/latex], Foci [latex]\\left(-4+\\sqrt{3},5\\right),\\left(-4-\\sqrt{3},5\\right)[\/latex]\n\"\"\n\n43.\u00a0Center [latex]\\left(-2,1\\right)[\/latex], Vertices [latex]\\left(0,1\\right),\\left(-4,1\\right),\\left(-2,5\\right),\\left(-2,-3\\right)[\/latex], Foci [latex]\\left(-2,1+2\\sqrt{3}\\right),\\left(-2,1 - 2\\sqrt{3}\\right)[\/latex]\n\"\"\n\n45.\u00a0Center [latex]\\left(-2,-2\\right)[\/latex], Vertices [latex]\\left(0,-2\\right),\\left(-4,-2\\right),\\left(-2,0\\right),\\left(-2,-4\\right)[\/latex], Focus [latex]\\left(-2,-2\\right)[\/latex]\n\"\"\n\n47.\u00a0[latex]\\frac{{x}^{2}}{25}+\\frac{{y}^{2}}{29}=1[\/latex]\n\n49.\u00a0[latex]\\frac{{\\left(x - 4\\right)}^{2}}{25}+\\frac{{\\left(y - 2\\right)}^{2}}{1}=1[\/latex]\n\n51.\u00a0[latex]\\frac{{\\left(x+3\\right)}^{2}}{16}+\\frac{{\\left(y - 4\\right)}^{2}}{4}=1[\/latex]\n\n53.\u00a0[latex]\\frac{{x}^{2}}{81}+\\frac{{y}^{2}}{9}=1[\/latex]\n\n55.\u00a0[latex]\\frac{{\\left(x+2\\right)}^{2}}{4}+\\frac{{\\left(y - 2\\right)}^{2}}{9}=1[\/latex]\n\n57.\u00a0[latex]\\text{Area}=12\\pi[\/latex] square units\n\n59.\u00a0[latex]\\text{Area}=2\\sqrt{5}\\pi[\/latex] square units\n\n61.\u00a0[latex]\\text{Area }9\\pi[\/latex] square units\n\n63.\u00a0[latex]\\frac{{x}^{2}}{4{h}^{2}}+\\frac{{y}^{2}}{\\frac{1}{4}{h}^{2}}=1[\/latex]\n\n65.\u00a0[latex]\\frac{{x}^{2}}{400}+\\frac{{y}^{2}}{144}=1[\/latex]. Distance = 17.32 feet\n\n67.\u00a0Approximately 51.96 feet","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0[latex]{x}^{2}+\\frac{{y}^{2}}{16}=1[\/latex]<\/p>\n

2.\u00a0[latex]\\frac{{\\left(x - 1\\right)}^{2}}{16}+\\frac{{\\left(y - 3\\right)}^{2}}{4}=1[\/latex]<\/p>\n

3.\u00a0center: [latex]\\left(0,0\\right)[\/latex]; vertices: [latex]\\left(\\pm 6,0\\right)[\/latex]; co-vertices: [latex]\\left(0,\\pm 2\\right)[\/latex]; foci: [latex]\\left(\\pm 4\\sqrt{2},0\\right)[\/latex]
\n\"\"<\/p>\n

4.\u00a0Standard form: [latex]\\frac{{x}^{2}}{16}+\\frac{{y}^{2}}{49}=1[\/latex]; center: [latex]\\left(0,0\\right)[\/latex]; vertices: [latex]\\left(0,\\pm 7\\right)[\/latex]; co-vertices: [latex]\\left(\\pm 4,0\\right)[\/latex]; foci: [latex]\\left(0,\\pm \\sqrt{33}\\right)[\/latex]
\n\"\"<\/p>\n

5.\u00a0Center: [latex]\\left(4,2\\right)[\/latex]; vertices: [latex]\\left(-2,2\\right)[\/latex] and [latex]\\left(10,2\\right)[\/latex]; co-vertices: [latex]\\left(4,2 - 2\\sqrt{5}\\right)[\/latex] and [latex]\\left(4,2+2\\sqrt{5}\\right)[\/latex]; foci: [latex]\\left(0,2\\right)[\/latex] and [latex]\\left(8,2\\right)[\/latex]
\n\"\"<\/p>\n

6.\u00a0[latex]\\frac{{\\left(x - 3\\right)}^{2}}{4}+\\frac{{\\left(y+1\\right)}^{2}}{16}=1[\/latex]; center: [latex]\\left(3,-1\\right)[\/latex]; vertices: [latex]\\left(3,-\\text{5}\\right)[\/latex] and [latex]\\left(3,\\text{3}\\right)[\/latex]; co-vertices: [latex]\\left(1,-1\\right)[\/latex] and [latex]\\left(5,-1\\right)[\/latex]; foci: [latex]\\left(3,-\\text{1}-2\\sqrt{3}\\right)[\/latex] and [latex]\\left(3,-\\text{1+}2\\sqrt{3}\\right)[\/latex]<\/p>\n

7. a.\u00a0[latex]\\frac{{x}^{2}}{57,600}+\\frac{{y}^{2}}{25,600}=1[\/latex]
\nb. The people are standing 358 feet apart.<\/p>\n

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

1.\u00a0An ellipse is the set of all points in the plane the sum of whose distances from two fixed points, called the foci, is a constant.<\/p>\n

3.\u00a0This special case would be a circle.<\/p>\n

5.\u00a0It is symmetric about the x<\/em>-axis, y<\/em>-axis, and the origin.<\/p>\n

7.\u00a0yes; [latex]\\frac{{x}^{2}}{{3}^{2}}+\\frac{{y}^{2}}{{2}^{2}}=1[\/latex]<\/p>\n

9.\u00a0yes; [latex]\\frac{{x}^{2}}{{\\left(\\frac{1}{2}\\right)}^{2}}+\\frac{{y}^{2}}{{\\left(\\frac{1}{3}\\right)}^{2}}=1[\/latex]<\/p>\n

11.\u00a0[latex]\\frac{{x}^{2}}{{2}^{2}}+\\frac{{y}^{2}}{{7}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(0,7\\right)[\/latex] and [latex]\\left(0,-7\\right)[\/latex]. Endpoints of minor axis [latex]\\left(2,0\\right)[\/latex] and [latex]\\left(-2,0\\right)[\/latex]. Foci at [latex]\\left(0,3\\sqrt{5}\\right),\\left(0,-3\\sqrt{5}\\right)[\/latex].<\/p>\n

13.\u00a0[latex]\\frac{{x}^{2}}{{\\left(1\\right)}^{2}}+\\frac{{y}^{2}}{{\\left(\\frac{1}{3}\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(1,0\\right)[\/latex] and [latex]\\left(-1,0\\right)[\/latex]. Endpoints of minor axis [latex]\\left(0,\\frac{1}{3}\\right),\\left(0,-\\frac{1}{3}\\right)[\/latex]. Foci at [latex]\\left(\\frac{2\\sqrt{2}}{3},0\\right),\\left(-\\frac{2\\sqrt{2}}{3},0\\right)[\/latex].<\/p>\n

15.\u00a0[latex]\\frac{{\\left(x - 2\\right)}^{2}}{{7}^{2}}+\\frac{{\\left(y - 4\\right)}^{2}}{{5}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(9,4\\right),\\left(-5,4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(2,9\\right),\\left(2,-1\\right)[\/latex]. Foci at [latex]\\left(2+2\\sqrt{6},4\\right),\\left(2 - 2\\sqrt{6},4\\right)[\/latex].<\/p>\n

17.\u00a0[latex]\\frac{{\\left(x+5\\right)}^{2}}{{2}^{2}}+\\frac{{\\left(y - 7\\right)}^{2}}{{3}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(-5,10\\right),\\left(-5,4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(-3,7\\right),\\left(-7,7\\right)[\/latex]. Foci at [latex]\\left(-5,7+\\sqrt{5}\\right),\\left(-5,7-\\sqrt{5}\\right)[\/latex].<\/p>\n

19.\u00a0[latex]\\frac{{\\left(x - 1\\right)}^{2}}{{3}^{2}}+\\frac{{\\left(y - 4\\right)}^{2}}{{2}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(4,4\\right),\\left(-2,4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(1,6\\right),\\left(1,2\\right)[\/latex]. Foci at [latex]\\left(1+\\sqrt{5},4\\right),\\left(1-\\sqrt{5},4\\right)[\/latex].<\/p>\n

21.\u00a0[latex]\\frac{{\\left(x - 3\\right)}^{2}}{{\\left(3\\sqrt{2}\\right)}^{2}}+\\frac{{\\left(y - 5\\right)}^{2}}{{\\left(\\sqrt{2}\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(3+3\\sqrt{2},5\\right),\\left(3 - 3\\sqrt{2},5\\right)[\/latex]. Endpoints of minor axis [latex]\\left(3,5+\\sqrt{2}\\right),\\left(3,5-\\sqrt{2}\\right)[\/latex]. Foci at [latex]\\left(7,5\\right),\\left(-1,5\\right)[\/latex].<\/p>\n

23.\u00a0[latex]\\frac{{\\left(x+5\\right)}^{2}}{{\\left(5\\right)}^{2}}+\\frac{{\\left(y - 2\\right)}^{2}}{{\\left(2\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(0,2\\right),\\left(-10,2\\right)[\/latex]. Endpoints of minor axis [latex]\\left(-5,4\\right),\\left(-5,0\\right)[\/latex]. Foci at [latex]\\left(-5+\\sqrt{21},2\\right),\\left(-5-\\sqrt{21},2\\right)[\/latex].<\/p>\n

25.\u00a0[latex]\\frac{{\\left(x+3\\right)}^{2}}{{\\left(5\\right)}^{2}}+\\frac{{\\left(y+4\\right)}^{2}}{{\\left(2\\right)}^{2}}=1[\/latex]; Endpoints of major axis [latex]\\left(2,-4\\right),\\left(-8,-4\\right)[\/latex]. Endpoints of minor axis [latex]\\left(-3,-2\\right),\\left(-3,-6\\right)[\/latex]. Foci at [latex]\\left(-3+\\sqrt{21},-4\\right),\\left(-3-\\sqrt{21},-4\\right)[\/latex].<\/p>\n

27.\u00a0Foci [latex]\\left(-3,-1+\\sqrt{11}\\right),\\left(-3,-1-\\sqrt{11}\\right)[\/latex]<\/p>\n

29.\u00a0Focus [latex]\\left(0,0\\right)[\/latex]<\/p>\n

31.\u00a0Foci [latex]\\left(-10,30\\right),\\left(-10,-30\\right)[\/latex]<\/p>\n

33.\u00a0Center [latex]\\left(0,0\\right)[\/latex], Vertices [latex]\\left(4,0\\right),\\left(-4,0\\right),\\left(0,3\\right),\\left(0,-3\\right)[\/latex], Foci [latex]\\left(\\sqrt{7},0\\right),\\left(-\\sqrt{7},0\\right)[\/latex]
\n\"\"<\/p>\n

35.\u00a0Center [latex]\\left(0,0\\right)[\/latex], Vertices [latex]\\left(\\frac{1}{9},0\\right),\\left(-\\frac{1}{9},0\\right),\\left(0,\\frac{1}{7}\\right),\\left(0,-\\frac{1}{7}\\right)[\/latex], Foci [latex]\\left(0,\\frac{4\\sqrt{2}}{63}\\right),\\left(0,-\\frac{4\\sqrt{2}}{63}\\right)[\/latex]
\n\"\"<\/p>\n

37.\u00a0Center [latex]\\left(-3,3\\right)[\/latex], Vertices [latex]\\left(0,3\\right),\\left(-6,3\\right),\\left(-3,0\\right),\\left(-3,6\\right)[\/latex], Focus [latex]\\left(-3,3\\right)[\/latex]
\nNote that this ellipse is a circle. The circle has only one focus, which coincides with the center.
\n\"\"<\/p>\n

39.\u00a0Center [latex]\\left(1,1\\right)[\/latex], Vertices [latex]\\left(5,1\\right),\\left(-3,1\\right),\\left(1,3\\right),\\left(1,-1\\right)[\/latex], Foci [latex]\\left(1,1+4\\sqrt{3}\\right),\\left(1,1 - 4\\sqrt{3}\\right)[\/latex]
\n\"\"<\/p>\n

41.\u00a0Center [latex]\\left(-4,5\\right)[\/latex], Vertices [latex]\\left(-2,5\\right),\\left(-6,4\\right),\\left(-4,6\\right),\\left(-4,4\\right)[\/latex], Foci [latex]\\left(-4+\\sqrt{3},5\\right),\\left(-4-\\sqrt{3},5\\right)[\/latex]
\n\"\"<\/p>\n

43.\u00a0Center [latex]\\left(-2,1\\right)[\/latex], Vertices [latex]\\left(0,1\\right),\\left(-4,1\\right),\\left(-2,5\\right),\\left(-2,-3\\right)[\/latex], Foci [latex]\\left(-2,1+2\\sqrt{3}\\right),\\left(-2,1 - 2\\sqrt{3}\\right)[\/latex]
\n\"\"<\/p>\n

45.\u00a0Center [latex]\\left(-2,-2\\right)[\/latex], Vertices [latex]\\left(0,-2\\right),\\left(-4,-2\\right),\\left(-2,0\\right),\\left(-2,-4\\right)[\/latex], Focus [latex]\\left(-2,-2\\right)[\/latex]
\n\"\"<\/p>\n

47.\u00a0[latex]\\frac{{x}^{2}}{25}+\\frac{{y}^{2}}{29}=1[\/latex]<\/p>\n

49.\u00a0[latex]\\frac{{\\left(x - 4\\right)}^{2}}{25}+\\frac{{\\left(y - 2\\right)}^{2}}{1}=1[\/latex]<\/p>\n

51.\u00a0[latex]\\frac{{\\left(x+3\\right)}^{2}}{16}+\\frac{{\\left(y - 4\\right)}^{2}}{4}=1[\/latex]<\/p>\n

53.\u00a0[latex]\\frac{{x}^{2}}{81}+\\frac{{y}^{2}}{9}=1[\/latex]<\/p>\n

55.\u00a0[latex]\\frac{{\\left(x+2\\right)}^{2}}{4}+\\frac{{\\left(y - 2\\right)}^{2}}{9}=1[\/latex]<\/p>\n

57.\u00a0[latex]\\text{Area}=12\\pi[\/latex] square units<\/p>\n

59.\u00a0[latex]\\text{Area}=2\\sqrt{5}\\pi[\/latex] square units<\/p>\n

61.\u00a0[latex]\\text{Area }9\\pi[\/latex] square units<\/p>\n

63.\u00a0[latex]\\frac{{x}^{2}}{4{h}^{2}}+\\frac{{y}^{2}}{\\frac{1}{4}{h}^{2}}=1[\/latex]<\/p>\n

65.\u00a0[latex]\\frac{{x}^{2}}{400}+\\frac{{y}^{2}}{144}=1[\/latex]. Distance = 17.32 feet<\/p>\n

67.\u00a0Approximately 51.96 feet<\/p>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Specific attribution<\/div>