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Solutions

Solutions to Try Its

1. Focus: $\left(-4,0\right)$; Directrix: $x=4$; Endpoints of the latus rectum: $\left(-4,\pm 8\right)$ 2. Focus: $\left(0,2\right)$; Directrix: $y=-2$; Endpoints of the latus rectum: $\left(\pm 4,2\right)$. 3. ${x}^{2}=14y$ 4. ${x}^{2}=14y$ 5. Vertex: $\left(8,-1\right)$; Axis of symmetry: $y=-1$; Focus: $\left(9,-1\right)$; Directrix: $x=7$; Endpoints of the latus rectum: $\left(9,-3\right)$ and $\left(9,1\right)$. 6. Vertex: $\left(-2,3\right)$; Axis of symmetry: $x=-2$; Focus: $\left(-2,-2\right)$; Directrix: $y=8$; Endpoints of the latus rectum: $\left(-12,-2\right)$ and $\left(8,-2\right)$. 7.  a. ${y}^{2}=1280x$ 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 $y=4\left(1\right){x}^{2}$ 9. yes ${\left(y - 3\right)}^{2}=4\left(2\right)\left(x - 2\right)$ 11. ${y}^{2}=\frac{1}{8}x,V:\left(0,0\right);F:\left(\frac{1}{32},0\right);d:x=-\frac{1}{32}$ 13. ${x}^{2}=-\frac{1}{4}y,V:\left(0,0\right);F:\left(0,-\frac{1}{16}\right);d:y=\frac{1}{16}$ 15. ${y}^{2}=\frac{1}{36}x,V:\left(0,0\right);F:\left(\frac{1}{144},0\right);d:x=-\frac{1}{144}$ 17. ${\left(x - 1\right)}^{2}=4\left(y - 1\right),V:\left(1,1\right);F:\left(1,2\right);d:y=0$ 19. ${\left(y - 4\right)}^{2}=2\left(x+3\right),V:\left(-3,4\right);F:\left(-\frac{5}{2},4\right);d:x=-\frac{7}{2}$ 21. ${\left(x+4\right)}^{2}=24\left(y+1\right),V:\left(-4,-1\right);F:\left(-4,5\right);d:y=-7$ 23. ${\left(y - 3\right)}^{2}=-12\left(x+1\right),V:\left(-1,3\right);F:\left(-4,3\right);d:x=2$ 25. ${\left(x - 5\right)}^{2}=\frac{4}{5}\left(y+3\right),V:\left(5,-3\right);F:\left(5,-\frac{14}{5}\right);d:y=-\frac{16}{5}$ 27. ${\left(x - 2\right)}^{2}=-2\left(y - 5\right),V:\left(2,5\right);F:\left(2,\frac{9}{2}\right);d:y=\frac{11}{2}$ 29. ${\left(y - 1\right)}^{2}=\frac{4}{3}\left(x - 5\right),V:\left(5,1\right);F:\left(\frac{16}{3},1\right);d:x=\frac{14}{3}$ 31.  33. 35. 37. 39. 41. 43.  45. ${x}^{2}=-16y$ 47. ${\left(y - 2\right)}^{2}=4\sqrt{2}\left(x - 2\right)$ 49. ${\left(y+\sqrt{3}\right)}^{2}=-4\sqrt{2}\left(x-\sqrt{2}\right)$ 51. ${x}^{2}=y$ 53. ${\left(y - 2\right)}^{2}=\frac{1}{4}\left(x+2\right)$ 55. ${\left(y-\sqrt{3}\right)}^{2}=4\sqrt{5}\left(x+\sqrt{2}\right)$ 57. ${y}^{2}=-8x$ 59. ${\left(y+1\right)}^{2}=12\left(x+3\right)$ 61. $\left(0,1\right)$ 63. At the point 2.25 feet above the vertex. 65. 0.5625 feet 67. ${x}^{2}=-125\left(y - 20\right)$, height is 7.2 feet 69. 2304 feet