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Study Guides > College Algebra

Solutions

Solutions to Try Its

1. Focus: (4,0)\left(-4,0\right); Directrix: x=4x=4; Endpoints of the latus rectum: (4,±8)\left(-4,\pm 8\right) 2. Focus: (0,2)\left(0,2\right); Directrix: y=2y=-2; Endpoints of the latus rectum: (±4,2)\left(\pm 4,2\right). 3. x2=14y{x}^{2}=14y 4. x2=14y{x}^{2}=14y 5. Vertex: (8,1)\left(8,-1\right); Axis of symmetry: y=1y=-1; Focus: (9,1)\left(9,-1\right); Directrix: x=7x=7; Endpoints of the latus rectum: (9,3)\left(9,-3\right) and (9,1)\left(9,1\right). 6. Vertex: (2,3)\left(-2,3\right); Axis of symmetry: x=2x=-2; Focus: (2,2)\left(-2,-2\right); Directrix: y=8y=8; Endpoints of the latus rectum: (12,2)\left(-12,-2\right) and (8,2)\left(8,-2\right). 7.  a. y2=1280x{y}^{2}=1280x b. The depth of the cooker is 500 mm

Solutions to Odd-Numbered Exercises

1. 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. 3. The graph will open down. 5. The distance between the focus and directrix will increase. 7. yes y=4(1)x2y=4\left(1\right){x}^{2} 9. yes (y3)2=4(2)(x2){\left(y - 3\right)}^{2}=4\left(2\right)\left(x - 2\right) 11. y2=18x,V:(0,0);F:(132,0);d:x=132{y}^{2}=\frac{1}{8}x,V:\left(0,0\right);F:\left(\frac{1}{32},0\right);d:x=-\frac{1}{32} 13. x2=14y,V:(0,0);F:(0,116);d:y=116{x}^{2}=-\frac{1}{4}y,V:\left(0,0\right);F:\left(0,-\frac{1}{16}\right);d:y=\frac{1}{16} 15. y2=136x,V:(0,0);F:(1144,0);d:x=1144{y}^{2}=\frac{1}{36}x,V:\left(0,0\right);F:\left(\frac{1}{144},0\right);d:x=-\frac{1}{144} 17. (x1)2=4(y1),V:(1,1);F:(1,2);d:y=0{\left(x - 1\right)}^{2}=4\left(y - 1\right),V:\left(1,1\right);F:\left(1,2\right);d:y=0 19. (y4)2=2(x+3),V:(3,4);F:(52,4);d:x=72{\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} 21. (x+4)2=24(y+1),V:(4,1);F:(4,5);d:y=7{\left(x+4\right)}^{2}=24\left(y+1\right),V:\left(-4,-1\right);F:\left(-4,5\right);d:y=-7 23. (y3)2=12(x+1),V:(1,3);F:(4,3);d:x=2{\left(y - 3\right)}^{2}=-12\left(x+1\right),V:\left(-1,3\right);F:\left(-4,3\right);d:x=2 25. (x5)2=45(y+3),V:(5,3);F:(5,145);d:y=165{\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} 27. (x2)2=2(y5),V:(2,5);F:(2,92);d:y=112{\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} 29. (y1)2=43(x5),V:(5,1);F:(163,1);d:x=143{\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} 31.  33. 35. 37. 39. 41. 43.  45. x2=16y{x}^{2}=-16y 47. (y2)2=42(x2){\left(y - 2\right)}^{2}=4\sqrt{2}\left(x - 2\right) 49. (y+3)2=42(x2){\left(y+\sqrt{3}\right)}^{2}=-4\sqrt{2}\left(x-\sqrt{2}\right) 51. x2=y{x}^{2}=y 53. (y2)2=14(x+2){\left(y - 2\right)}^{2}=\frac{1}{4}\left(x+2\right) 55. (y3)2=45(x+2){\left(y-\sqrt{3}\right)}^{2}=4\sqrt{5}\left(x+\sqrt{2}\right) 57. y2=8x{y}^{2}=-8x 59. (y+1)2=12(x+3){\left(y+1\right)}^{2}=12\left(x+3\right) 61. (0,1)\left(0,1\right) 63. At the point 2.25 feet above the vertex. 65. 0.5625 feet 67. x2=125(y20){x}^{2}=-125\left(y - 20\right), height is 7.2 feet 69. 2304 feet

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