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{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "C
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"" }{TEXT 259 20 "Exercise 19, p. 223." }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 1619 "restart:\nn:=19:\na:=-2:\nb:=1:\nc:=8:\nh:=-3:\nk:=2:\nr:=sq
rt(5):\nxleft:=-6:\nxright:=6:\nybot:=-6:\nytop:=10:\nf:=x->solve(a*x+
b*y=c,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\n
g2:=x->op(2,[g(x)]):\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x
):\nF:=(x,y)->(x-h)^2+(y-k)^2:\n#x2:=x1:\ny1:=f(x1):\ny2:=f(x2):\n`Exe
rcise `||n||`. Graph the following line and circle, and then find any \+
points of intersection.`;\ny=f(x),`  `*(x-h)^2+(y-k)^2=r^2;\n#y=f(x),`
  `*y=g1(x),`  `*y=g2(x);\n#`Intersection Points: `*[x1,y1]=evalf([x1,
y1],3),[x2,y2]=evalf([x2,y2],3);\np[0]:=plot(f(x),x=xleft..xright,y=yb
ot..ytop,color=blue):\np[1]:=plot(g1(x),x=xleft..xright,y=ybot..ytop,c
olor=navy):\np[2]:=plot(g2(x),x=xleft..xright,y=ybot..ytop,color=navy)
:\np[3]:=plot([[x1,y1]],style=point,symbol=circle,color=red):\np[4]:=p
lot([[0,y1],[x1,y1]],linestyle=2,color=red):\np[5]:=plot([[x1,y1],[x1,
0]],linestyle=2,color=red):\np[6]:=plot([[x2,y2]],style=point,symbol=c
ircle,color=red):\np[7]:=plot([[0,y2],[x2,y2]],linestyle=2,color=red):
\np[8]:=plot([[x2,y2],[x2,0]],linestyle=2,color=red):\nCombinedPlot:=p
lots[display](\n               [seq(p[i],i=0..8)],\n                sc
aling=constrained,\n                labels=[``,``],\n                #
tickmarks=[5,9],\n                #view=[x_left..x_right,y_vertex-20..
y_vertex+20],\n                titlefont=[HELVETICA,DEFAULT,14],\n    \+
            title=`Chapter 6.2, Exercise `||n):\nCombinedPlot;\n`Subst
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)=r^2;\nexpand(F(x,f(x)))-r^2=0;\nx=x1,x2,` `*y=y1,y2;\n`Intersection \+
Points: `*[x[1],y[1]]=evalf([x1,y1],3),[x[2],y[2]]=evalf([x2,y2],3);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExercise~19.~Graph~the~following~
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"Curve 9" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%-Substitute:~G\"\"\"%
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{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&\"\"&\"\"\")%\"xG\"\"#F'F'*&\"#IF
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\"xG\"\"#F'F'*&\"#IF'F)F'F'\"#SF'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6&/%\"xG!\"#!\"%/*&%\"~G\"\"\"%\"yGF*\"\"%\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$/*&%6Intersection~Points:~G\"\"\"7$&%\"xG6#F&&%\"yGF*
F&7$$!\"#\"\"!$\"\"%F0/7$&F)6#\"\"#&F,F67$$!\"%F0$F0F0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 33 "Chapter 6.2, Exercise 27, p. 223." }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 258 20 "Exercise 27, p. 223." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 1636 "restart:\nn:=27:\na:=1:\nb:=1:\nc:=23:\nh:=0:\nk:
=0:\nr:=sqrt(289):\nf:=x->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-
k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)]):\nx1:=op(1,[so
lve(f(x)=g1(x),x)]):\nx2:=op(2,[solve(f(x)=g1(x),x)]):\nF:=(x,y)->(x-h
)^2+(y-k)^2:\nx1:=op(1,[solve(f(x)=g1(x),x)]):\nx2:=op(2,[solve(f(x)=g
1(x),x)]):\ny1:=f(x1):\ny2:=f(x2):\nxleft:=-20:\nxright:=20:\n`Exercis
e `||n||`. Graph the following line and circle, and then find any poin
ts of intersection.`;\ny=f(x),`  `*(x-h)^2+(y-k)^2=r^2;\n#y=f(x),`  `*
y=g1(x),`  `*y=g2(x);\n#`Intersection Points: `*[x1,y1]=evalf([x1,y1],
3),[x2,y2]=evalf([x2,y2],3);\np[0]:=plot(f(x),x=xleft..xright,color=bl
ue):\np[1]:=plot(g1(x),x=xleft..xright,color=navy):\np[2]:=plot(g2(x),
x=xleft..xright,color=navy):\np[3]:=plot([[x1,y1]],style=point,symbol=
circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]],linestyle=2,color=red)
:\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,color=red):\np[6]:=plot([[x
2,y2]],style=point,symbol=circle,color=red):\np[7]:=plot([[0,y2],[x2,y
2]],linestyle=2,color=red):\np[8]:=plot([[x2,y2],[x2,0]],linestyle=2,c
olor=red):\nCombinedPlot:=plots[display](\n               [seq(p[i],i=
0..8)],\n                scaling=constrained,\n                labels=
[``,``],\n                #tickmarks=[5,9],\n                #view=[x_
left..x_right,y_vertex-20..y_vertex+20],\n                titlefont=[H
ELVETICA,DEFAULT,14],\n                title=`Chapter 6.2, Exercise `|
|n):\nCombinedPlot;\n`Substitute: `*y=f(x),` into `*F(x,y)=r^2;\nF(x,f
(x))=r^2;\nexpand(F(x,f(x)))=r^2;\nexpand(F(x,f(x)))-r^2=0;\nx=x1,x2,`
 `*y=y1,y2;\n`Intersection Points: `*[x[1],y[1]]=evalf([x1,y1],3),[x[2
],y[2]]=evalf([x2,y2],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExerci
se~27.~Graph~the~following~line~and~circle,~and~then~find~any~points~o
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4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" }}}{PARA 11 "" 1 
"" {XPPMATH 20 "6$/*&%-Substitute:~G\"\"\"%\"yGF&,&%\"xG!\"\"\"#BF&/*&
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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&\"\"#\"\"\")%\"xGF&F'F'*&\"#YF'
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{XPPMATH 20 "6&/%\"xG\"\")\"#:/*&%\"~G\"\"\"%\"yGF*F&F%" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$/*&%6Intersection~Points:~G\"\"\"7$&%\"xG6#F&&%
\"yGF*F&7$$\"\")\"\"!$\"#:F0/7$&F)6#\"\"#&F,F67$F1F." }}}{EXCHG {PARA 
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"Chapter 6.2, Exercise 28, p. 223." }}{EXCHG {PARA 0 "" 0 "" {TEXT 
262 20 "Exercise 28, p. 223." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }{MPLTEXT 1 0 1540 "restart:\nn:=28:\na:=-8:\nb:=9:\nc:=10:\nh
:=0:\nk:=0:\nr:=10:\nf:=x->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y
-k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)]):\nx1:=solve(f
(x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x):\ny1:=f(x1):\ny2:=f(x2):\nF:=(x
,y)->(x-h)^2+(y-k)^2:\n`Exercise `||n||`. Graph the following line and
 circle, and then find any points of intersection.`;\ny=f(x),`  `*(x-h
)^2+(y-k)^2=r^2;\n#y=f(x),`  `*y=g1(x),`  `*y=g2(x);\n#`Intersection P
oints: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=evalf([x2,y2],3);\np[0]:=plo
t(f(x),x=-12..12,color=blue):\np[1]:=plot(g1(x),x=-12..12,color=navy):
\np[2]:=plot(g2(x),x=-12..12,color=navy):\np[3]:=plot([[x1,y1]],style=
point,symbol=circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]],linestyle
=2,color=red):\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,color=red):\np
[6]:=plot([[x2,y2]],style=point,symbol=circle,color=red):\np[7]:=plot(
[[0,y2],[x2,y2]],linestyle=2,color=red):\np[8]:=plot([[x2,y2],[x2,0]],
linestyle=2,color=red):\nCombinedPlot:=plots[display](\n              \+
 [seq(p[i],i=0..8)],\n                scaling=constrained,\n          \+
      labels=[``,``],\n                #tickmarks=[5,9],\n            \+
    #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n               \+
 titlefont=[HELVETICA,DEFAULT,14],\n                title=`Chapter 6.2
, Exercise `||n):\nCombinedPlot;\n`Substitute: `*y=f(x),` into `*F(x,y
)=r^2;\nF(x,f(x))=r^2;\nexpand(F(x,f(x)))=r^2;\nexpand(F(x,f(x)))-r^2=
0;\n(81/5)*(expand(F(x,f(x)))-r^2)=0;\nx=x1,x2,` `*y=y1,y2;\n`Intersec
tion Points: `*[x[1],y[1]]=evalf([x1,y1],3),[x[2],y[2]]=evalf([x2,y2],
3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExercise~28.~Graph~the~follo
wing~line~and~circle,~and~then~find~any~points~of~intersection.G" }}
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{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%-Substitute:~G\"\"\"%\"yGF&,&*(\"
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1 "" {XPPMATH 20 "6#/,(*&#\"$X\"\"#\")\"\"\"*$)%\"xG\"\"#F)F)F)*&#\"$g
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X\"\"#\")\"\"\"*$)%\"xG\"\"#F)F)F)*&#\"$g\"F(F)F,F)F)#\"%+!)F(!\"\"\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&\"#H\"\"\")%\"xG\"\"#F'F'*
&\"#KF'F)F'F'\"%+;!\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&/%\"xG
#\"$+#\"#H!\")/*&%\"~G\"\"\"%\"yGF,#\"$5#F'!\"'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$/*&%6Intersection~Points:~G\"\"\"7$&%\"xG6#F&&%\"yGF*F&
7$$\"$!p!\"#$\"$C(F0/7$&F)6#\"\"#&F,F67$$!\")\"\"!$!\"'F<" }}}{EXCHG 
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-1 33 "Chapter 6.2, Exercise 29, p. 223." }}{EXCHG {PARA 0 "" 0 "" 
{TEXT 263 20 "Exercise 29, p. 223." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 1642 "restart:\nn:=29:\na:=2:\nb:=-1:\nc:=
7:\nh:=0:\nk:=0:\nr:=sqrt(7):\nxleft:=-10:\nxright:=10:\nytop:=-10:\ny
bot:=10:\nf:=x->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^2,y
):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)]):\n#x1:=solve(f(x)=g1(x),
x):\n#x2:=solve(f(x)=g2(x),x):\nx1:=0:\nx2:=0:\n#y1:=f(x1):\n#y2:=f(x2
):\ny1:=0:\ny2:=0:\nF:=(x,y)->(x-h)^2+(y-k)^2:\n`Exercise `||n||`. Gra
ph the following line and circle, and then find any points of intersec
tion.`;\ny=f(x),`  `*(x-h)^2+(y-k)^2=r^2;\n#y=f(x),`  `*y=g1(x),`  `*y
=g2(x);\n#`Intersection Points: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=eva
lf([x2,y2],3);\np[0]:=plot(f(x),x=xleft..xright,y=ytop..ybot,color=blu
e):\np[1]:=plot(g1(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[2]:
=plot(g2(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[3]:=plot([[x1
,y1]],style=point,symbol=circle,color=red):\np[4]:=plot([[0,y1],[x1,y1
]],linestyle=2,color=red):\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,co
lor=red):\np[6]:=plot([[x2,y2]],style=point,symbol=circle,color=red):
\np[7]:=plot([[0,y2],[x2,y2]],linestyle=2,color=red):\np[8]:=plot([[x2
,y2],[x2,0]],linestyle=2,color=red):\nCombinedPlot:=plots[display](\n \+
              [seq(p[i],i=0..8)],\n                scaling=constrained
,\n                labels=[``,``],\n                #tickmarks=[5,9],
\n                #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n \+
               titlefont=[HELVETICA,DEFAULT,14],\n                titl
e=`Chapter 6.2, Exercise `||n):\nCombinedPlot;\n`Substitute: `*y=f(x),
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(x,f(x)))-r^2=0;\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x):\n
x=op(1,[x2]),op(2,[x2]);\n`No Intersection Points.`;" }}{PARA 11 "" 1 
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" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "Chap
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Exercise 30, p. 223." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 1 0 1624 "restart:\nn:=30:\na:=1:\nb:=2:\nc:=10:\nh:=0:\nk:=0
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->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^2,y):\ng1:=x->op(
1,[g(x)]):\ng2:=x->op(2,[g(x)]):\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(
f(x)=g2(x),x):\nx2:=x1:\ny1:=f(x1):\ny2:=f(x1):\nF:=(x,y)->(x-h)^2+(y-
k)^2:\n`Exercise `||n||`. Graph the following line and circle, and the
n find any points of intersection.`;\ny=f(x),`  `*(x-h)^2+(y-k)^2=r^2;
\n#y=f(x),`  `*y=g1(x),`  `*y=g2(x);\n#`Intersection Points: `*[x1,y1]
=evalf([x1,y1],3),[x2,y2]=evalf([x2,y2],3);\np[0]:=plot(f(x),x=xleft..
xright,y=ytop..ybot,color=blue):\np[1]:=plot(g1(x),x=xleft..xright,y=y
top..ybot,color=navy):\np[2]:=plot(g2(x),x=xleft..xright,y=ytop..ybot,
color=navy):\np[3]:=plot([[x1,y1]],style=point,symbol=circle,color=red
):\np[4]:=plot([[0,y1],[x1,y1]],linestyle=2,color=red):\np[5]:=plot([[
x1,y1],[x1,0]],linestyle=2,color=red):\np[6]:=plot([[x2,y2]],style=poi
nt,symbol=circle,color=red):\np[7]:=plot([[0,y2],[x2,y2]],linestyle=2,
color=red):\np[8]:=plot([[x2,y2],[x2,0]],linestyle=2,color=red):\nComb
inedPlot:=plots[display](\n               [seq(p[i],i=0..8)],\n       \+
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p:=-20:\nybot:=20:\nf:=x->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-
k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)]):\nx1:=solve(f(
x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x):\n#x2:=x1:\ny1:=f(x1):\ny2:=f(x2
):\nF:=(x,y)->(x-h)^2+(y-k)^2:\n`Exercise `||n||`. Graph the following
 line and circle, and then find any points of intersection.`;\ny=f(x),
`  `*(x-h)^2+(y-k)^2=r^2;\n#y=f(x),`  `*y=g1(x),`  `*y=g2(x);\n#`Inter
section Points: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=evalf([x2,y2],3);\n
p[0]:=plot(f(x),x=xleft..xright,y=ytop..ybot,color=blue):\np[1]:=plot(
g1(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[2]:=plot(g2(x),x=xl
eft..xright,y=ytop..ybot,color=navy):\np[3]:=plot([[x1,y1]],style=poin
t,symbol=circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]],linestyle=2,c
olor=red):\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,color=red):\np[6]:
=plot([[x2,y2]],style=point,symbol=circle,color=red):\np[7]:=plot([[0,
y2],[x2,y2]],linestyle=2,color=red):\np[8]:=plot([[x2,y2],[x2,0]],line
style=2,color=red):\nCombinedPlot:=plots[display](\n               [se
q(p[i],i=0..8)],\n                scaling=constrained,\n              \+
  labels=[``,``],\n                #tickmarks=[5,9],\n                \+
#view=[x_left..x_right,y_vertex-20..y_vertex+20],\n                tit
lefont=[HELVETICA,DEFAULT,14],\n                title=`Chapter 6.2, Ex
ercise `||n):\nCombinedPlot;\n`Substitute: `*y=f(x),` into `*F(x,y)=r^
2;\nF(x,f(x))=r^2;\nexpand(F(x,f(x)))=r^2;\nexpand(F(x,f(x)))-r^2=0;\n
(4)*(expand(F(x,f(x)))-r^2)=0;\nx=x1,x2,` `*y=y1,y2;\n`Intersection Po
ints: `*[x[1],y[1]]=evalf([x1,y1],3),[x[2],y[2]]=evalf([x2,y2],3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExercise~31.~Graph~the~following~li
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%\"xGF&F,#F&F+F,/*&%'~into~GF&,&*$)F-F+F&F&*$)F'F+F&F&F&\"$p\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$)%\"xG\"\"#\"\"\"F)*$),&*(\"\"&F)
F(!\"\"F'F)F/#F)F(F/F(F)F)\"$p\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,
(*&#\"#H\"\"%\"\"\"*$)%\"xG\"\"#F)F)F)*&#\"\"&F-F)F,F)F)#F)F(F)\"$p\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*&#\"#H\"\"%\"\"\"*$)%\"xG\"\"#
F)F)F)*&#\"\"&F-F)F,F)F)#\"$v'F(!\"\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,(*&\"#H\"\"\")%\"xG\"\"#F'F'*&\"#5F'F)F'F'\"$v'!\"\"
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&/%\"xG!\"&#\"$N\"\"#H/*&%\"~G
\"\"\"%\"yGF,\"#7#!$_$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%6Inter
section~Points:~G\"\"\"7$&%\"xG6#F&&%\"yGF*F&7$$!\"&\"\"!$\"#7F0/7$&F)
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{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "Chapter 6.2
, Exercise 32, p. 223." }}{EXCHG {PARA 0 "" 0 "" {TEXT 261 20 "Exercis
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estart:\nn:=32:\na:=0:\nb:=1:\nc:=5:\nh:=2:\nk:=3:\nr:=2:\nxleft:=-5:
\nxright:=5:\nytop:=-5:\nybot:=5:\nf:=x->solve(a*x+b*y=c,y):\ng:=x->so
lve((x-h)^2+(y-k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)])
:\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x):\nx2:=x1:\ny1:=f(
x1):\ny2:=f(x2):\nF:=(x,y)->(x-h)^2+(y-k)^2:\n`Exercise `||n||`. Graph
 the following line and circle, and then find any points of intersecti
on.`;\ny=f(x),`  `*(x-h)^2+(y-k)^2=r^2;\n#y=f(x),`  `*y=g1(x),`  `*y=g
2(x);\n#`Intersection Points: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=evalf
([x2,y2],3);\np[0]:=plot(f(x),x=xleft..xright,y=ytop..ybot,color=blue)
:\np[1]:=plot(g1(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[2]:=p
lot(g2(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[3]:=plot([[x1,y
1]],style=point,symbol=circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]]
,linestyle=2,color=red):\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,colo
r=red):\np[6]:=plot([[x2,y2]],style=point,symbol=circle,color=red):\np
[7]:=plot([[0,y2],[x2,y2]],linestyle=2,color=red):\np[8]:=plot([[x2,y2
],[x2,0]],linestyle=2,color=red):\nCombinedPlot:=plots[display](\n    \+
           [seq(p[i],i=0..8)],\n                scaling=constrained,\n
                labels=[``,``],\n                #tickmarks=[5,9],\n  \+
              #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n     \+
           titlefont=[HELVETICA,DEFAULT,14],\n                title=`C
hapter 6.2, Exercise `||n):\nCombinedPlot;\n`Substitute: `*y=f(x),` in
to `*F(x,y)=r^2;\nF(x,f(x))=r^2;\nexpand(F(x,f(x)))=r^2;\nexpand(F(x,f
(x)))-r^2=0;\nx=x1,x2,` `*y=y1,y2;\n`Intersection Point: `*[x[1],y[1]]
=evalf([x1,y1],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExercise~32.~
Graph~the~following~line~and~circle,~and~then~find~any~points~of~inter
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3;4#yN1X&zBF07$Ffcl$\"3k+B60y:fCF07$F[dl$\"33b7uC/.aDF07$F`dl$\"3QeO*=
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\\uF\\u-%&STYLEG6#%&POINTG-%'SYMBOLG6#%'CIRCLEG-F$6%7$7$F\\uF+Fb`mFe`m
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ELSG6%%!GF]bm-%%FONTG6#%(DEFAULTG-%(SCALINGG6#%,CONSTRAINEDG-%&TITLEG6
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Facm" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1
" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8
" "Curve 9" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%-Substitute:~G\"\"
\"%\"yGF&\"\"&/*&%'~into~GF&,&*$),&%\"xGF&\"\"#!\"\"F1F&F&*$),&F'F&\"
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\"\"\"\"#!\"\"F*F)F)\"\"%F)F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$
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{XPPMATH 20 "6#/,(*$)%\"xG\"\"#\"\"\"F)*&\"\"%F)F'F)!\"\"F+F)\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6&/%\"xG\"\"#F%/*&%\"~G\"\"\"%\"yGF)\"\"
&F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%5Intersection~Point:~G\"\"
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0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "Chapte
r 6.2, Exercise 33, p. 223." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 257 20 "Exercise 33, p. 223." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
1651 "restart:\nn:=33:\na:=-sqrt(3):\nb:=1:\nc:=0:\nh:=0:\nk:=4:\nr:=4
:\nxleft:=-6:\nxright:=6:\nybot:=-6:\nytop:=10:\nf:=x->solve(a*x+b*y=c
,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x
->op(2,[g(x)]):\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x):\n#
x2:=x1:\ny1:=f(x1):\ny2:=f(x2):\nF:=(x,y)->(x-h)^2+(y-k)^2:\n`Exercise
 `||n||`. Graph the following line and circle, and then find any point
s of intersection.`;\ny=f(x),`  `*(x-h)^2+(y-k)^2=r^2;\n#y=f(x),`  `*y
=g1(x),`  `*y=g2(x);\n#`Intersection Points: `*[x1,y1]=evalf([x1,y1],3
),[x2,y2]=evalf([x2,y2],3);\np[0]:=plot(f(x),x=xleft..xright,y=ybot..y
top,color=blue):\np[1]:=plot(g1(x),x=xleft..xright,y=ybot..ytop,color=
navy):\np[2]:=plot(g2(x),x=xleft..xright,y=ybot..ytop,color=navy):\np[
3]:=plot([[x1,y1]],style=point,symbol=circle,color=red):\np[4]:=plot([
[0,y1],[x1,y1]],linestyle=2,color=red):\np[5]:=plot([[x1,y1],[x1,0]],l
inestyle=2,color=red):\np[6]:=plot([[x2,y2]],style=point,symbol=circle
,color=red):\np[7]:=plot([[0,y2],[x2,y2]],linestyle=2,color=red):\np[8
]:=plot([[x2,y2],[x2,0]],linestyle=2,color=red):\nCombinedPlot:=plots[
display](\n               [seq(p[i],i=0..8)],\n                scaling
=constrained,\n                labels=[``,``],\n                #tickm
arks=[5,9],\n                #view=[x_left..x_right,y_vertex-20..y_ver
tex+20],\n                titlefont=[HELVETICA,DEFAULT,14],\n         \+
       title=`Chapter 6.2, Exercise `||n):\nCombinedPlot;\n`Substitute
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;\nexpand(F(x,f(x)))-r^2=0;\n(1/4)*(expand(F(x,f(x)))-r^2)=0;\nx=x1,x2
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[2],y[2]]=evalf([x2,y2],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExer
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{PARA 3 "" 0 "" {TEXT -1 34 "Chapter 6.2, Exercise 34, p. 223.\n" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 265 20 "Exercise 34, p. 223." }{TEXT -1 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1669 "restart:\nn:=34:\na:=1:\nb
:=-1:\nc:=3:\nh:=5:\nk:=-2:\nr:=4:\nxleft:=-5:\nxright:=10:\nytop:=-10
:\nybot:=5:\nf:=x->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^
2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)]):\nx1:=op(1,[solve(f(x
)=g1(x),x)]):\nx2:=op(2,[solve(f(x)=g1(x),x)]):\n#x2:=x1:\ny1:=f(x1):
\ny2:=f(x2):\nF:=(x,y)->(x-h)^2+(y-k)^2:\n`Exercise `||n||`. Graph the
 following line and circle, and then find any points of intersection.`
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[1]:=plot(g1(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[2]:=plot(
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style=point,symbol=circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]],lin
estyle=2,color=red):\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,color=re
d):\np[6]:=plot([[x2,y2]],style=point,symbol=circle,color=red):\np[7]:
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2,0]],linestyle=2,color=red):\nCombinedPlot:=plots[display](\n        \+
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lf([x2,y2],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%fpExercise~34.~Grap
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{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$),&%\"xG\"\"\"\"\"&!\"\"\"\"#F)F)
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{XPPMATH 20 "6#/,(*&\"\"#\"\"\")%\"xGF&F'F'*&\"#7F'F)F'!\"\"\"#5F'\"\"
!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$)%\"xG\"\"#\"\"\"F)*&\"\"'F)
F'F)!\"\"\"\"&F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&/%\"xG\"\"\"
\"\"&/*&%\"~GF%%\"yGF%!\"#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&
%6Intersection~Points:~G\"\"\"7$&%\"xG6#F&&%\"yGF*F&7$$F&\"\"!$!\"#F//
7$&F)6#\"\"#&F,F57$$\"\"&F/$F6F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 37 "___________________
__________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 30 "Filename: ExplorePrecalc04.mws" }}{PARA 0 "" 0 "" {TEXT 
-1 36 "Copyright 2005, All Rights Reserved." }}{PARA 0 "" 0 "" {TEXT 
-1 44 "Permission is granted to use and modify for " }}{PARA 0 "" 0 "
" {TEXT -1 37 "academic and non-commercial purposes." }}{PARA 0 "" 0 "
" {TEXT -1 13 "Dr. John Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "Mathemati
cs Department-MICDS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@micds
.org or pais@kinetigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL:  http
://kinetigram.com/micds" }}{PARA 0 "" 0 "" {TEXT -1 37 "______________
_______________________" }}}{MARK "116 0 0" 34 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }