6.1: Conic Sections
- Page ID
- 143134
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Find the value of \(c\) so that the quadratic expression \(x^2 + 8x + c\) factors into a perfect square.
- Find the value of \(c\) so that the quadratic expression \(x^2 - 9x + c\) factors into a perfect square.
- Find the value of \(c\) so that the quadratic expression \(x^2 + \dfrac{4}{3}x + c\) factors into a perfect square.
- Plot \(y = 3x^2\).
- Plot \(x = -\dfrac{3}{2}y^2\).
- Plot \(x^2 + y^2 = 4\).
- Plot \(\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1\).
- plot \(\dfrac{x^2}{9} - \dfrac{y^2}{4} = 1\).
- plot \(\dfrac{y^2}{4} - \dfrac{x^2}{16} = 1\).
- Plot \(y = -2(x - 4)^2 - 3\).
- Plot \(x = 3\left(y + \dfrac{1}{2}\right)^2 + 1\).
- Plot \( (x + 3)^2 + y^2 = \dfrac{25}{4}\).
- Plot \(\dfrac{(x - 1)^2}{4} + \dfrac{\left(y + \frac{5}{2}\right)^2}{16} = 1\).
- Plot \(\dfrac{(x + 3)^2}{9/4} - \dfrac{(y + 2)^2}{49/4} = 1\).
- Plot \(\dfrac{\left(y-\frac{1}{2}\right)^2}{25} - \left(x - \frac{3}{2}\right)^2 = 1\).
- Plot \(-2x^2 -16x - 2y - 24 = 0\).
- Plot \(-2y^2 + 2x + 12y - 20 = 0\).
- Plot \(-3x^2 - 3y^2 - 12y - 9 = 0\).
- Plot \(16x^2 + y^2 + 64x + 6y + 57 = 0\).
- Plot \(27x^2 - 48y^2 - 162x - 189 = 0\).
- Plot \(-16x^2 + 4y^2 + 32x - 16y - 64 = 0\).