Search

Text Color

Margin Size

Font Type

Enable Dyslexic Font

13.4: Introduction to Conics- Answers to the Homework Exercises

Last updated

Oct 3, 2021
Save as PDF
- 13.3: Parabolas
- Back Matter

$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$

$\newcommand{\id}{\mathrm{id}}$ $\newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $\newcommand{\range}{\mathrm{range}\,}$

$\newcommand{\RealPart}{\mathrm{Re}}$ $\newcommand{\ImaginaryPart}{\mathrm{Im}}$

$\newcommand{\Argument}{\mathrm{Arg}}$ $\newcommand{\norm}[1]{\| #1 \|}$

$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$\newcommand{\Span}{\mathrm{span}}$

$\newcommand{\id}{\mathrm{id}}$

$\newcommand{\Span}{\mathrm{span}}$

$\newcommand{\kernel}{\mathrm{null}\,}$

$\newcommand{\range}{\mathrm{range}\,}$

$\newcommand{\RealPart}{\mathrm{Re}}$

$\newcommand{\ImaginaryPart}{\mathrm{Im}}$

$\newcommand{\Argument}{\mathrm{Arg}}$

$\newcommand{\norm}[1]{\| #1 \|}$

$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$\newcommand{\Span}{\mathrm{span}}$ $\newcommand{\AA}{\unicode[.8,0]{x212B}}$

$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vectorC}[1]{\textbf{#1}}$

$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$

$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$

$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$

$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$

$\newcommand{\avec}{\mathbf a}$

$\newcommand{\bvec}{\mathbf b}$

$\newcommand{\cvec}{\mathbf c}$

$\newcommand{\dvec}{\mathbf d}$

$\newcommand{\dtil}{\widetilde{\mathbf d}}$

$\newcommand{\evec}{\mathbf e}$

$\newcommand{\fvec}{\mathbf f}$

$\newcommand{\nvec}{\mathbf n}$

$\newcommand{\pvec}{\mathbf p}$

$\newcommand{\qvec}{\mathbf q}$

$\newcommand{\svec}{\mathbf s}$

$\newcommand{\tvec}{\mathbf t}$

$\newcommand{\uvec}{\mathbf u}$

$\newcommand{\vvec}{\mathbf v}$

$\newcommand{\wvec}{\mathbf w}$

$\newcommand{\xvec}{\mathbf x}$

$\newcommand{\yvec}{\mathbf y}$

$\newcommand{\zvec}{\mathbf z}$

$\newcommand{\rvec}{\mathbf r}$

$\newcommand{\mvec}{\mathbf m}$

$\newcommand{\zerovec}{\mathbf 0}$

$\newcommand{\onevec}{\mathbf 1}$

$\newcommand{\real}{\mathbb R}$

$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$

$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$

$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$

$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$

$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$

$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$

$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$

$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$

$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$

$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$

$\newcommand{\bcal}{\cal B}$

$\newcommand{\ccal}{\cal C}$

$\newcommand{\scal}{\cal S}$

$\newcommand{\wcal}{\cal W}$

$\newcommand{\ecal}{\cal E}$

$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$

$\newcommand{\gray}[1]{\color{gray}{#1}}$

$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$

$\newcommand{\rank}{\operatorname{rank}}$

$\newcommand{\row}{\text{Row}}$

$\newcommand{\col}{\text{Col}}$

$\renewcommand{\row}{\text{Row}}$

$\newcommand{\nul}{\text{Nul}}$

$\newcommand{\var}{\text{Var}}$

$\newcommand{\corr}{\text{corr}}$

$\newcommand{\len}[1]{\left|#1\right|}$

$\newcommand{\bbar}{\overline{\bvec}}$

$\newcommand{\bhat}{\widehat{\bvec}}$

$\newcommand{\bperp}{\bvec^\perp}$

$\newcommand{\xhat}{\widehat{\xvec}}$

$\newcommand{\vhat}{\widehat{\vvec}}$

$\newcommand{\uhat}{\widehat{\uvec}}$

$\newcommand{\what}{\widehat{\wvec}}$

$\newcommand{\Sighat}{\widehat{\Sigma}}$

$\newcommand{\lt}{<}$

$\newcommand{\gt}{>}$

$\newcommand{\amp}{&}$

$\definecolor{fillinmathshade}{gray}{0.9}$

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

$(x+1)^2+(y+5)^2=100$
$clipboard_e2daa35634f0d90ea4180c59fb0414183.png$
Figure 13.4.1

$(x+3)^2+\left(y-\dfrac{7}{13}\right)^2=\dfrac{1}{4}$
$clipboard_e768f1240e6276acda885c9d9e032c77c.png$
Figure 13.4.2

$(x+9)^2+y^2=25$ ; center $(-9,0)$ , radius $r=5$
$clipboard_eb22b0537bc1cd95fb115438068d6abf7.png$
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 $r=\dfrac{\sqrt{30}}{2}$
$clipboard_e27e1b5abe53502c73483aabb6de7ac6a.png$
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 $r=\dfrac{\sqrt{161}}{10}$
$clipboard_e48ea4b708e6e51e741d3546bacbebf60.png$
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 $y=4$
$clipboard_e6548057fdda420a45893ccba380f6787.png$
Figure 13.4.6

Vertex $(-3,2)$ ; Focus $(-6,2)$ ; Directrix $x=0$
$clipboard_eaa495579a3d2b13cdfab0a89bbaa9500.png$
Figure 13.4.7

Vertex $(1,-3)$ ; Focus $(1,-2)$ ; Directrix $y=-4$
$clipboard_ed327db463912a90f3ec9a28f1898bbb2.png$
Figure 13.4.8

Vertex $(2,4)$ ; Focus $\left(\dfrac{13}{2},4\right)$ ; Directrix $x=-\dfrac{5}{2}$
$clipboard_e6f71ae9faee62fe289f7aa215019d4be.png$
Figure 13.4.9

$(x+1)^2=8(y-6)$ ; Vertex $(-1,6)$ ; Focus $(-1,8)$ ; Directrix $y=4$
$clipboard_e436d72e3336e0a259b565f0254e84164.png$
Figure 13.4.10

$(y+1)^2=-\dfrac{1}{2}(x-10)$ ; Vertex $(10,-1)$ ; Focus $\left(\dfrac{79}{8},-1\right)$ ; Directrix $x=\dfrac{81}{8}$
$clipboard_e1616b4c5ffc259dbaa5dbcb832ed3d55.png$
Figure 13.4.11

Introduction to Conics

Circles

Parabolas

Support Center

How can we help?