3ข9-10-64

11 11 1 1 XX X X
Y
LL L X X XLX Y Y X(0,Yb) (0, b) (0, bX) X
0 X X X bX X0Y X (X0, bY) Xb b(0X, b)b
L bLb 00b L

b b0 0 Y XY Y X X Xb Y b

YY (0,b) L L (0,bL)

(0,b)
(0,b)

(0,b)X L X

0 X 0 X

X y = b Y (0,b) 0(0, b) 0 L

X

X 0X b X

Y0

(0,b) L

b0 b0 X X

b0 X Y

b0 b0 Xb 0 XY X

Y

0 LX

0 LX

y=b=0 LX

0

b0 Y X X b

b0 X X Xb b

b b 0 0b 0 X XX X b bX b

b0Y Y X X

0 X
L
X 0 X (0,b) X
X L X
(0,b) Y 0 (0, b)
Xb

Y y = b (0,b) L

(0,b) L
0 X

X (x, y) R  R y

X (x, y) R  R y =(bx, y) R  R y =Xb (x, y )  y b = b

R  R y = b R Ry

y b (x, y) R  R y = b yb

X (0, 3)

X 33((x3x31,,X3yy{XX)){({x((x{,xR,R(y,xyb)yb,)b4)yR(4R(0b)4R0,Ry3,3y34RL3L3=)R=)3LR3R33L3Ryy3Ry=={y=((770x=,7,347Y)y43()0,yy3)=y{=RXX(=−yx−X1,1−=}y}XR1b)−}XX41yXX}RXX=3LXX7R(Xxy(,x(X=y,xXX),y7X(Xyy)xX),RX=yRX)−RR(y10}RR,(y=0R3(X,=0)y−33,y313R=)(}3=)0(33,y033X,(X=)X303,)(330()0,4,33)(4)
X
X (0, 34) 4

−1}

X
X

−1}

X

b3 {(x, y ) R  b 3 y = −1} X X 3X
L RXy = 7L

X3 X (x, y) R  R Xy = 3(x, y) R 

, y) R  R y = 3 X (0X, 3) 4

(0, 3) {(x, y)4R  R y = 7 {(x, yy)=−R1} R y = 7 y = −1}

6 66 5255 X 6 5 XXX XXX

X XXX

X 6 LLL XXX L 6 66 X

X (x, y) R  R y = −6 XXX (x((,xxy,,)yy))RRRRRRy yy===−6−−66

55 (x, y) R  R y = −6 XX XX
66
XX XX 66
LL
XX ((xx,,yy))RRRRyy==−−66

22 2 L YY (a, 0)
YY XY (a, 0) X aY
L a 0 Y YX a
a 0L (Ya, 0)
a0 YYY YY YY Y a
Y L
L L YX L (a, 0) (a, 0)
X
a0 Y Y LY aY

a0 Y

YL L

Y (0a,0) (a,0)X X
(a,0) X
Y X (a, 0) 0
Y Y 0 X X
0
(a,0a) (a,0)

L 0

x=a

a0 Y
aa 00 YY Y

YY L

LL

0 X
00 XX

x=a=0

a0 Y Y a
a
a0 a 0 L YY Y Y a

Y X Y
X
LY
L

Y X (a, 0) a0 X
Y (a,0) Y (0a,0)

L (a,0) 0

x=a

(a,0) X

Y (x, y) R  R x =

Y (x, y) R  R x = aY (x,y(x),y)RRRxR=xa= a
(x, y) R  R x = a (x, y)x Ra R x = a
xa

Y (3,4)

4 34 4 YY (3,4)
44 Y6 6 (3,4)(3,4)
Y (x, y )Y Ra6=R 3a6=a 6 (3,4) 6 YY
Y 3=
Y 3 6 a=3 RRy((33)Yaa,,44R==)()3Ra33,4Y=) R(33366a,4Y=)Y6Y663

−3} a =(a33,=4L)3 L 6 Y Y((LxYx,,yy(x)),yRR)(xYY, = −3}x = −3}
YY Y
Y LL x YY Y
Y Y 9

Y  {(x(,x{{y,)((xxy{R,,)(yyxR)){,xR(y=x)9RR,yR()R3RRxa,4=xx=R−)R3==}3x99R= Y 6
9xx6==x−−{{=33(}(}x−xx,,3yY=}y))−YR3}RRx R= 9x = 9 x
=

−3} 4 4 (3,4) Y (3,4) Y

Y 6(3,4) 6

a=3 a=3 Y Y6

L YL

Y6 Y (x, y) R  R a = 3Y (x, y)

x, y) R  R a = 3 Y (3,4) Y 6

(3,4{()x, y) R 6R x = 9 {x(=x,−y3)} R  R x = 9 x = −3}

6 466 10 6 Y YY Y
10 1100 Y
L LL Y Y YY L10 1100 Y
Y Y YY
10 Y YY (x,(y(x)x,,yy)R)RRRxRR=x1x0==1100

Y (x, y) R  R x = 10 (x, y) R  R x = 10

6 Y
10
Y Y 10
L
Y (x, y) R  R x = 10

(x, y) R  R y1 − y2

3 XY

L XY Y ชm ผ (x1, y1 ) (x2 , y2

(x, y) R  R y1 − y2 = m(x1 − x2 ) ๆ L

ถ (x, y)

(x1, y1 ) (x2, y2 ) m = y1 − y2 y1 − y2m= =m(xy1 −−xy2 1) y − y1 = m(x − x1 )
x1 − x2 x − x1
(x, y)

1 m= y − y1 y− y1 = m(x − x1(x),Xy) R  (-1, 0−) y2 = m(x1 −
ช x − x1 8
0 R y1

01 8

ช m ช ผm (ผx1, y1 ) ((xx21,, yy21)) m= y
x
(x, y)(x,Ry)RRx=Ray − y1 =Ym(x −(xx1,)y) R  R x = a
Y

(x, y) R  R x = a m = y − y1 x(yx−,ayy)1= Rm(xR−(xxx,1=y))aR  R y − 0 x= 8(xa + 1)
x y = 8x + 8
−(xx1, y) R R

X XY Y

YY ชชnnAnn AAmผmผCชชmCชmxyชxyAAyyCCyxCyxCyyxmCymCymAA(A(mผA(xmผxxxCxmผxCbmm0ผb0mbC0,,Cxbm,bymxbyyyxxyyyA))A)bbyAbAyCyyCyxyxCyCCmYYCyyxymxYCyCymm((x(xxA(AxbxA0xxb0,xbb0,(b0b,(y(b,0yb0y0)y,b,),)bb)bbb)))YYYYAAA(A((000(,,,0bbb,))b) )

n
n

ถ x 0 yb ผy 0, b
ผ ชYy
0 y bถ x y ผ 0mx y by 0,bb 0m, b
0,ชb m
mx ผ b y 0, b y mxช b Ym Y

ช m (x, y) R YR y1 − 0y,2b= m(x1 − x2 )
  R y1 − y2 = m(x1 − x2 ()x, y) R  R y1 − y2 = m(x1 − x2 )

1 y = mx + c m ช

12 y = mx + c Ax + Bmy + C = 0 ช A,cB,C
y = mx +12c
m Byy,AC==,ชB−2−2,BCABAชxmxช−−c=ACถABCถyB−yxx=+B=A+c−2BmBBAyyx+++mxCC−c==CถB=Y−00BA mY A, B,C c

Ax + By +2C = 0 A, ช

y = mx + c m ช A, B,C

2 Axถ+ By + C = 0 Y c = − CY c=−
B
= 2− A x −ถ C
B B Y c=−C
A C B
= − B xm− − A ช Y −cC=m−=CB− A
B= B B
A Y c
m=− =
BB

51 X (-1, 0)

X )=ผ8(R(xx1,(+y-111R)1,(()ช10xxy),((1R−ชช,xxชyy,,)((y110(ชyyx1)ชRx,)),-11,=1Ryyy)(8)0m((ช)xRR=xx(,(R,,ชช8xx(yR((yy01,xRx,)xxy−RR)),yy1,,+1−Yy))xy1yyyR(8)R1R8))xRRy−−),(1y((R(Ryชxชxxyxyy(R=−R,RRช,,)x−11,RRyyy80,ymy==RชyR()y)y)yy)10R(yRR1mR88−00)mm,xyy===01−=8y(RymR((−Ryy=−R−)8x088mxx(810RymR=((−0011,x=xXxyy0xx1yyyx−−(=y,1(8801,,1xy11R++R8RR=()x=y)=01=8xx0(yxym01x−−==R=−x=)88x11−y88y))m,yyผ+525252(,))8+x080y8mmx8yyRx=x=−y−((28(0x121x8)x8Rx1x(ช(8x−−)RR)88x−)xyy,−+((−(0101−+-x1x1xyyRxx−−ชช51=R8152181x,R),R2+=m=+,RR()1xy)xyy0)(=x20ช88)808101mmXy82ช8)))1yy=mm))R−R−80,m)R((=y−−8xx5XX4((ym(ช101R0R1y8mxxx00)ผx−−(R01−x,,X−x+−ชช==x=yxy,0+yผmผRR01818)x8y)88()−−)−8=1-8)((X=yymmผ1)xxผ5208,R8R(((−−++XX(0--x=(R11x)00x1ช1ผ1ชY,,(=,((8+))-Rช00+=y=Rxx1())5ผ21ผ1R11x,1(8y8),,m)y(m(0x)+yy((-xym−)11−xxX111X1,)),(−,((0y++X)0--0(yx11010)=1111)=,,((,)ผ))ผ00=x8xy88))ผ11(8(,,

mช

y(x−,0y

(x(x, ,yy))RRRRyy−=08=x8+(x8+1)

(x, y) R  R y = 8x + 8

6 ผ (2,0) (4,5)

ชชชช ช yymmyymmyy−−yy−−==−=−=−−yyyyy01yyyx01y0yx1yyxy01yyx111111=======11=====−−===−−−−−−m52m52m5252525252x5252ymxyx52y5252(x2(yx22(xx2yyyy2x(xx2xxx(x2x(x2xx−x−−====−x−−−−−−−−−5−5=55552222−5252x52=2525x=21152xxxx)(x(20y21m))(22201−−−−)y)(−220−−)))2−−=5555)−5−4−)y54y01y5y4x11=====−−=−−=m525252xy−−52(2−(x2−xx52x−52−−−==5=52x2=52521=)(20)52252−−)22222222222254yyyyyyyy0000yyyy===============2222111155555522220000xxxxxx−−55552222xxxx−−−−−−xxxx52−−−−11112222−−−−00001111yyyy00005555−−−−=1111520000
(2,0)

5x − 2y −10 = 0 s

7 ผ (3,2) (1,8)

ชชชชช (3,2)333333xxxxxx ++++++yyyyyymmmmmmyyyyyyyyyyyyyyyyyy−−−−−−======−−−−−−−−−−−−−−−−−−yyyyyy111111222222111111yyyyyyxxxxxx222222yyyyyyyyyy1111111111111111================================−−−−−−−−−−mmmmmm((((((−−−−−−−−−−−−−−−−000000xxxxxxyyyyyy−−−−−−333333((((((3333332222223333222222333333xxxxxxxxxxxxxxxxxxxxxx))))))−−−−−−((((((++++++++++++++++xxxxxx======xxxxxx111111999999−−−−−−999999111111111111222222333333))))))++++++333333−−−−−−−−−−))))))222222111111888888 ====== −−−−−−222222666666 ====== −−−−−−333333

8 ผ (-3,5) (4,8)
ชชชช (4,8) 33333yyyymmmmxxxxxyyyy−−−−−−−−−====−−−−yyyy7777777778888111117777yyyyxxxx7777yyyyy1111111111yyyyy=yyy=======yyyy−−−−−−−−+++++−−−−−−−−−−−−mmmm77773333xxxx44444yyyy((((777755555555(((((72(((777222244444222226666xxxx00006666xyxxxyyy))))=8===888−−−−−−−−========================00000xxxx4444333333333333333311111))))−−−−xxxx((((((((xxxxxxxx))))55557777xxxx−−−−3333++++−−−−))))−−−−−−−−1111−−−−1111777733334444888822224444222244444444(((())))xxxx++++−−−−−−−−55557777====66664444yyyy−−−−−−−−)))) 77773333 ==== 77773333

8.

X y = .....

Y ช x = ..... m = y1 − y2 = 5 − 8
x1 − x2 − 3 − 4

XY y − y1 = m(x − x1 )

y − 8 = 3 (x − 4)

7

7 y − (7)8 = (7) 3 (x −
7
1 y = mx + c m 7 y −ช56 = 3(cx
y = mx +12 c − 4)
ช Ayxc+= Bmyx++Cc = 0 Ym A,7By,C−ช56 = 3cx −12
m

Ax + By +2C = 0 A,ชB2,C c Aถx + By + C =Y 0 A, B,C 7 y = 3x −12 +
= mx + c m 0 = 3x + 44 −
y
2 Ax +ถBy + C = 0 3x − 7 y + 44 = 0
A, By, C= −2 A x − ถCB C
B
y2= − A ถx − C y=−Ax−C A
B B

AAAAAAAAAAxxxxxxxxxx++++++++++BBBBBBBBBByyyyyyyyyy++++++++++BBBBBCCCCCCCCCCyyyyyyyyyy=====ชชช==============0000000000−−−−−−−−−−mmmmAAAAABBBBBAAAAAxxxxx====xxxxx−−−−−−−−−−−−−−CCCCCAAAAABBBBCCCCCAAAAABBBBB,,,,, BBBBB,,,,,CCCCC y = mmmmxxxx ++++ cccc CCCCCB
yyy === BBB
cccc = −
YYYYY === −−−

12 2 (x, y) R  R y = 2x + 3
cm(x,(yx,)ym)R(xRช,Ry ) R  R y = 2x
R R y = 2x + 32 ช y mx c +
y 2x y 3 mx
ช 2 Ry 2ช=x2+x3+3
y=
2 ชyy)=ช2Rx +
2 myy myyช2mmm2yyxชx2m2xชชx23m22mcyyxxmy3cช22m32xcชx222xm322(cxm3, ym2)2Rmช(Rx, 3Ry = 2x + 3ช
ช

2ช ชY 2Yx + 3y − 6 = 20x + 3y − 6 = 0

− 6= 0 ชช−−ช223xx++6222mmm6322xxxmxx===++++=2+−−−333x32−3yyy332232xy+y22−−−m333+−3xyyy−3666yyyyyyy36=y+===6yYY3y===y======−==−Yyy3===−−−−6−−−−−−000y0==233−−−06222222=222y333y−3−−333322xxxxxx=2xxx3yyy0==236yyxx2+++x+++30+++x===x−−+===+666+222+2−666333−−+26YY−−2023mx623xY222x6332x3+x3x+x=222A+mx+62+xxx++x+63−3+6=x+++3+((636y23200063+−y(Y333B,,,−03222−3yyy32,yy6yy))2y6−−−+=)===−=666C−−−0(600====222,3=32xx0000x)0+++6263Y22222xxxmmmxxAm+++mm+AAAx2===+333(=Axxxx=32=+0Am3−−−yyyx,x−y++++xAm2B−y−2−−−233232=++−x332+)yBBBx−23BmA=666−y3+6B+yyyB+6−y===A−32y==By+++C3c=x−326c+000y+0−yCCC==+06=+=CC−322===0=B−C06==yC000B0==00+020Cxm=+Am=03x
3y =
=
y

3

3 33333322x222222x2+x22222xxxxx+xxxxxx3++++++X3+(+++++3333333033333yX3(XXXXX)33333(((((0−00000y−yyyyy)222222222)))))6−222222226−−−−−−xxxxxxxxxxx−−−−−2xxxxxxxx222226=6=++++++++66666==xx=66666xXxxxxxxxxxxxxxxx++++++++X=0=033333333=======y3======662X==========XXXXXX=====33333333XXXX(((((((X00XXXXX0000000=y30000066000002yyyyyyyyyyy333336666666666222223)))))))=0−−−−−−−−−−−−−=====(22222222330666666666666600000xxxxxxxxxxxxxx2xxxxxx,((((((203========x=====33333====================XXXXXXX2,)x,,,,,0XXXXXX+2000000000000000000xyyyyyyyy3333333366666666666622222222+)x)))))3+========X3(+03y00000000X3)((((((((0−−33333333yY2),,,,,,,,6600000000−−xxxYYYYYY2)))))))==6=6==XxxxX0=0=y36==62=XX0=0y36620=YYYYYY(30,(032),x202222222()+x20xxxxx22222x2()22222+3(((((0++++++x00000+xxxxxy)3)))))33333Y+33++++++−y+++++YyyyyyyyY33YYYYY33333−62222222233333−−−−−Y−y−3yyyyyyxxxxxxxx22222222yyyyy6=yy66666−6y222222226−(((((((3−−−−−++++++++−−−−−3333300000000==yy=0Yxxxxxxxx=====yyyyyyyyyy6==y6=66666yyyyy)))))))3333333366666==0++++++++2Y63++++++++==========00000==6YYYY0yyyyyyyy=0===============xY3YYYYY333333326333333333−−−−−−−−6222220666663333306666600000yyyyyyyy00000x=yyyyyyyyxxxxx66666666(−−−−−−−−−0−−−−−−−333=3333302============yyyyyyyyyyyyyy(,66666666yyyyyyyy(((((6026666666x2000000000002========0======000000YYYYYYY,2)(===============,,,,,+2========0x222222x222222226666666633333333)266666666000)000003)))))(00000000++0xxxxxxxx+xy)3Y3========+3−+y(((((((yy00000000Y30000000063−−,,,,,,,,−3y22222222y=yy66y)))))))6−−3==0Y=yy==6=y6

4 2x −244443xy−−−ช4m=3334yyyyช4yy=4ชชช===4==2=232x23−−ช222−−44mxชxxx2−x232−−ช−−−−−A−x−−ช=−−ชชช2x3−ชmx2mmm3x3333+33x23333y+−xyyy+34yyyyyyyyy2yyy−y+yyyx=yy−===−4ช=24=x==m========−−====−3−======ช3−B3x432323232−m4−y−yy2ช3y323322233−−−y−−−−−−y3−−−3=−−−y−m−4444344ช3yyy3=3==my2222y=y=3xxxx=+23232332=2222yyy3−−−−3y32−−−−yy===yyyxxxx=yxxxx−−−−32==−y−y−−==xxxCx===42224232=3333=+++=+===++++232=−−−xxx−x=x+++=343234432+4344−322332−−−=−444x4442444x324−x−−32−2−−x44−−−2−2−3x+22x444−04+2x−x−x232+43x−2x3333x−3−2+x4x2+x−4x3+34x+2−x+3+x+443+4x+43X−4−34444−3−3443y3=m22242=xxx2x−−−x−−m2Y333−3xBAA2yyy=3y−2x2x===y−x=3x+−=444−y−423−B222423=2x3yyxxx3mmmyx−y4+m−−−=−=3AAA=2===C333A4=yxxx3xyyy44m−−−x223=y−+++−−22===x+Am=4=0x−B−−BB3xm−m444222x−By=yyy−−−3334A2=3+yAA3=+=++x033Xy−+xx−B===yCCCy+−−42=+=+Cy3==322323−B===+42−B−B32=4y4232m000=yCy33+0++=23==C=C=CXXX−023Y=X32B=32A=000Xmmm

ช

4 (ตอ่ )

XY

X X YYY2YxXXXY22Y−2xxXX3x2XX2−−XXxyx−Xx2X3322X=2=x=−3Y2YxxyyXXxxxx−yx4342X42====X==−3xy==2x=y44xy42243244x2Y==2=4244xx=xy==xx=X((yy4X424=−X22(=Y=y−04=244xx2==,,3x22002(y3=,24244==20xyyx))00xxyx=x=X,)0x0===22−=(y=2===22)0=3x4x02244=,442X420xyXx2−=)0y==(y=322x2=x4=,xy424x0=0==)=0=y222x424=4x=X0X(y−22x3=,20xy=x)0===2 y=0
XXX
YX 4 −−2YY22323xx2yxyy2−−x−−YYYY−x=−==YY−33−33YY−3−34−YYyyyy324yy3yyy3y3xy2y43======y=y=y2x=−x=−=YY44−−044x=−=−4=−YY3,4−34−4334−−3YY3y4−y234y4034xx34y3y3yx00x=x=43=0y0y==,,y==−=−−−YYx==,,4−04=−−==0034−344334=,0043y−34y434−y43420x==43=x430x0=,x4−=−,−4−0YY−0=,4303343−34xyy0y0

4 x2=x
4
2 (2,0)

X X (2,0X) (2X,0) (2,0) (2,0)

−=X63=2YX066X00=ช012C=..1221121223=32........3xAX222xxyx33ชxY2ชชชช640,43214003y,..3yAX4y1225x33333x3B3333..AAAAyXXX3xxxx2x122xxxxx3333x..6.xช216ช2xxxx624−3..ชชช4=6Y2y44444,6433334y4444Xyyyy6321,,,,3ชyB=y4444yyyy3YX300AX..x3ชBBBB2Xxyyyy0333303x3A6Xxx6xxxx−x33x6666xxxx4444=636666Y6AXX−−−−4x6xช3ชC=yyyyy4====x6666333YYYXAX633ช4444x6666ช4=34yx−−−−XYx2=30xxXXXX,36666333344y====xyXy0ชxXYXYXYYX30,ช000066664B64y3yAX33XXXX0000ช34x00004By4====yyxY3,32x,34y4646yC0,=xy4xx6,40000B0−06y4yBx34CCCCy====633yชy=y2−6xYB4yx463y3y==xy6x3333Y642222x4−=xxxx4666Xyx4x63x−,6xxxxyyyy−==−64yXx3y4y63XY=606Y6y=yY−=62646YB6XY0yX64636y0y=0,6640−=21YXYYYY42222X−6=34=060X00=x666663..0,000,,,4−==XY=06Xyx46444463YX66000000000=6−03X6y0XY00yyyy6XCyy0=0=066=0Yx3C333X4=60=0=3−==ชXxxxx206=3x6312=2C0x=xyXY06C..0366666=xy644332CX==03412122102x=3=3ช2......=yxYx343y4442AX23Yxx206xy0,60y3yyyx3xy40,ช03C04=000000Yx2y6=yY320,32Yx462630400,6xy340,3x43206666y40x3Ay0X0ช,x3y4yyx633336ชชชช3Y2x333B3AAAy63xxxx0,x4xxx333x4060x64x4yxxx663y6−43y00y4y,=6Y4444y46x3334y4444−=ByyyXy0633,,,=y6444yyyyXY060x0664BBB6yyyYXx4333060−4=xxxชชyy6=643Y666yxxxx4444466660−−−066−=XC=ชyyyy63yyyy====666=444666YX06=ชช364−−−−====2XXXxYX6666333300===xy6=YXXYYX00032666666664444YYYXXX000430000ช====(Y2C=44443333600,4=000030,02CCxC====yxy232====33332222xxx)xxxyyy(Y323322232600,640,0(((YYY2222y666000000,,,,44423000,,,0000yyy)043222333436)))436664343ช

9. ล็ ิช

m= A Ax − By + C = 0
B Ax + By + C = 0

m=−A
B

1 ช5 ผ (4,8)

m=5 6
6
5x − 6y + C = 0
ผ (4,8)
5(4) − 6(8) + C = 0

20 − 48 + C = 0
− 28 + C = 0
C = 28

5x − 6y + 28 = 0

2222222222 2(m((2mm(m22(m(2mm,(2((m2mmm3m=,,2m,2233==m,(3m=,)m3=m,m3=m=,,))23=)=3=3==yx)=)yymxx,=11)=yx))3=72yx=111==yx772211yxyyxx−−)11721172=−−−(72m111111−−y7x277222−−−−xy−−11−−−−xxm,7yy2x2y3=2xy−−x22y22x2yxx2)yy222=2ผ2222xy22ผผ=2ผ==ผ11222ผ27=222ผ=xผผ2=222xx−−23=2=2=(22x22233ผ2x((−2x32(2223=−−−−x222x2x3(xy(−−−2−23)2233−2(2−((−−27))x−2−2252−9−24−−−7722−)223−55)−99x7−−44(−−2−−)(27y594xx7−)−25))−294((22yy−5−x2974ผ77−−7=−−−(xy5−945−−522x99−44(y−−77−==+()2y−−−2x2,−xx17=7(−−(2y++−((yy7−=23,,2511947−−=+((−−−23−−27,−−2323−−1x227+7=x1(77==,+−331−−77(32,y(1−−−)1277311+(332++)7−,−−3127,,11))−32111(77y((−7−=37))7−321217)−2−−33227+177yy3+1))+733−+−−−77777122)−−++177,7)y111++++)(7172)y+11))3+27y2+7C+2)=+))37727++C+7−++−y7=77yyCC+1+5C==C9472+−7722+++CC1)C==++=++CC++CCx+)CC=+=C(CyC7C=yC=0+C7C−C2++CCC=+=CC=C−C2==++700C27=CC=C==−CC==CC=CC=C07722=C=++=0,C====17=20C==(CC=C712====32=0CC7200===3===0711===−−=77277012=02===1C700==1=)====001000=)01770=0070y7=21==7=001107200+==0(07++0700000((00009077=701+(C99=0(000C(=90,0CC97(((95,,0C9,95590,5,(=)725=,5,,=))9=55)5)=1),0))5)0070)(9,5)
ผผผผผผผผผผ ผ

−0−66666662ผ2x3x333333ผ3+yyyyy3yy+yy5−−−−−−−53−−=2222222=y2((2xxxxxxx0−00x0((((((x(+,++++++00,00002+−0−+,,,,,,5,555x5552−−−−−−502000000−0xxxxxxx5x)2+)=22222======2=−−−−−−−ผ−−−−−−−−−)=))))))500000000(yyyyyyyyyy0yyyyyy0YY=YYYYY2−−2−−⊥⊥−−−−−−−−−−−⊥⊥⊥⊥⊥,−−(−−−−−−−x00x22222222222222226222222,−−−==)==3===========333333======233y0(3yy00yyyyy)(y000000(((((yyyyyyy0y000000−0300000y3−,−−−−−−2(,2−−(,,,,,22−−02−22−−222−−−02(x22222225x5(222)−((((((222)222)2x2xxxxxx−−2222232−−−−−−3)+2+x=y))))))+=x+2yx++++++222222)xyyyyyy3(5+−20)2+0+)))0)))5++y5+55555++++++(=33+(3,++++++3Y5−−−=−30(2x======3333332y0x(3Y02333333YYYYY322x=0y+xxxxxx5−0y(−000)0002(((−(((())22222)0+00030000++++++C0++=y++y5)yyyyyYy)))))))xYCCCCCCC+3CC2−+C0−=⊥C+++++++=+Y++−+YYYYYYx(C=(2302CCCCCCC−======2=033333CC=CCC2=2=x+x(2(xxxxx0==((((((=030y00000=−=00=======x0)2=====+xxxxxx+++++y20+(y0+00y=0000004===0===44444)4−)44444CC,+0+02−00000=2=====)C))))))(2=C=xx2−0)00000−0+2=0y=xxxxxxx)y5+0−0+−−−−−−−=3y3Yyyyyyy2x0(2−0−−−−−−=+y)22222220C++Y=======C=3C0000000x(0==x+0=440=) x

x − y− 2=

0) ผผผผ 33yy 0
4= ผผ
0 ผ

3y − 2x +5 = 0 2x − 3y − 5 = 0C C= 4= 4

2y32x+y+3+x23+yx4++=C40= 0

ผ (0,−2) 3(0) + 2(−2) + C = 0

ฝึ ห 15