13.4: Introduction to Conics- Answers to the Homework Exercises
- Page ID
- 45126
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Introduction to Conics
- \(\left(0,\dfrac{1}{2}\right)\); \(\sqrt{109}\approx 10.44\)
- \(\left(-\dfrac{1}{2},-\dfrac{3}{2}\right)\); \(\sqrt{34}\approx 5.83\)
- \(\left(\dfrac{185}{2},-69\right)\); \(41\)
- circle
- ellipse
- parabola
- parabola
Circles
- \((x+1)^2+(y+5)^2=100\)
Figure 13.4.1
- \((x+3)^2+\left(y-\dfrac{7}{13}\right)^2=\dfrac{1}{4}\)
Figure 13.4.2
- \((x+9)^2+y^2=25\); center \((-9,0)\), radius \(r=5\)
Figure 13.4.3
- \(\left(x+\dfrac{5}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{30}{4}\); center \(\left(-\dfrac{5}{2},\dfrac{1}{2}\right)\), radius \(r=\dfrac{\sqrt{30}}{2}\)
Figure 13.4.4
- \(\left(x+\dfrac{1}{2}\right)^2+\left(y-\dfrac{3}{5}\right)^2=\dfrac{161}{100}\); center \(\left(-\dfrac{1}{2},\dfrac{3}{5}\right)\), radius \(r=\dfrac{\sqrt{161}}{10}\)
Figure 13.4.5
- \((x-3)^2+(y-6)^2=20\)
- \((x-1)^2+\left(y-\dfrac{3}{2}\right)^2=\dfrac{13}{2}\)
Parabolas
- Vertex \((3,0)\); Focus \((3,-4)\); Directrix \(y=4\)
Figure 13.4.6
- Vertex \((-3,2)\); Focus \((-6,2)\); Directrix \(x=0\)
Figure 13.4.7
- Vertex \((1,-3)\); Focus \((1,-2)\); Directrix \(y=-4\)
Figure 13.4.8
- Vertex \((2,4)\); Focus \(\left(\dfrac{13}{2},4\right)\); Directrix \(x=-\dfrac{5}{2}\)
Figure 13.4.9
- \((x+1)^2=8(y-6)\); Vertex \((-1,6)\); Focus \((-1,8)\); Directrix \(y=4\)
Figure 13.4.10
- \((y+1)^2=-\dfrac{1}{2}(x-10)\); Vertex \((10,-1)\); Focus \(\left(\dfrac{79}{8},-1\right)\); Directrix \(x=\dfrac{81}{8}\)
Figure 13.4.11