Solutions
Solutions to Try Its
1. Focus: [latex]\left(-4,0\right)[/latex]; Directrix: [latex]x=4[/latex]; Endpoints of the latus rectum: [latex]\left(-4,\pm 8\right)[/latex]
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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 [latex]y=4\left(1\right){x}^{2}[/latex] 9. yes [latex]{\left(y - 3\right)}^{2}=4\left(2\right)\left(x - 2\right)[/latex] 11. [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] 13. [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] 15. [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] 17. [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] 19. [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] 21. [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] 23. [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] 25. [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] 27. [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] 29. [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] 31.
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