Grapes/win 2.8
[Don't Edit] 3.14
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BGstretchOn BGfile
0 
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UserFunction
2 1 2 1 1
xSqrt(1-x^2)
cosx
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y = f(x)
0
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0 = f(x,y)
1 1 0
x^2/a^2 +(y-f(a))^2/f(a)^2 =1
0 16711680 2 1 4 1 0 1
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Point
22 3 4 5 6 7 8 0 1 9 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
P
1 3 2
Q
2a^2-1
2f(a)
0


t 0.1
0 0
48896 16711680 16777215 1 0 0 1 1 0
2 0 1
Q
1 1 2
P
-P.x
P.y
0


t 0.1
0 0
16711680 16711680 16777215 1 0 0 1 1 0
1 0 1
R
1 8 2
A
-1
0
0


t 0.1
0 0
48896 16711680 16777215 1 0 0 1 1 0
2 0 1
S
1 9 2
S
a
f(a)
0


t 0.1
0 0
255 16711680 16777215 0 0 0 1 1 0
3 0 1
T
1 8 2
T
-S.x
S.y
0


t 0.1
0 0
255 16711680 16777215 0 0 0 1 1 0
3 0 1
U
1 0 2
U
(rot(P,R,-karg(RP))).x
(rot(P,R,-karg(RP))).y
0


t 0.1
1 0
48896 16711680 16777215 0 0 0 1 1 0
2 0 1
V
0 0 1
A
2 0 2
A
0
0
1


t 0.1
0 0
16777215 16711680 16777215 1 0 0 1 1 0
3 0 2
B
1 9 2
B
1
0
0


t 0.1
0 0
255 255 16777215 1 0 0 1 1 0
1 0 2
C
0 0 1
D
0 0 1
E
0 0 1
F
0 0 1
G
0 0 1
H
0 0 1
I
0 0 1
J
0 0 1
K
0 0 1
L
0 0 1
M
0 0 1
N
0 0 1
O
1 0 2
O
0
0
0


t 0.1
0 0
16777215 16711680 16777215 1 0 0 1 1 0
3 0 1
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Segments
7
7 1 1 13631696 16777215 1 0 1
0 
1 2 3 9 0 0 0 0 0 0 0
1 1 1 48896 16777215 4 0 1
0 
1 3 0 0 0 0 0 0 0 0 0
1 1 1 255 16777215 3 0 1
7 {2a}
5 4 0 0 0 0 0 0 0 0 0
1 1 1 48896 16777215 4 0 0
0 
3 6 0 0 0 0 0 0 0 0 0
1 1 1 0 16777215 3 0 0
0 
5 3 0 0 0 0 0 0 0 0 0
1 1 1 0 16777215 3 0 0
0 
4 6 0 0 0 0 0 0 0 0 0
1 1 1 255 16777215 1 0 1
0 
3 9 0 0 0 0 0 0 0 0 0
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paramater
14
0.94 0
1 1 0.02 1
0.43 0
1 1 0.01 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
1 0
1 1 0.1 1
-0.6 0
1 1 0.1 1
1 0
1 1 0.05 0
1 1 80
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KakuMode ScanWidth LogMode ThetaMode AreaMode capStyle
1 4 2 1 1 0 0 1 0 0 0
DrawMode SegmentShowSync
1 0
AfterImageColorNo, CanAImg
2 1
circleMode
1
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ScaleX
Vlow,VHigh,label
0 932 x
x
AxesVisible,ScaleVisible,Svaluevisible,AddDegreeLetter,ScaleGuidevisible
0 0 0 0 0
NUmber,Base,Linterval
1 1 1
High,Low
1.29148574812895 -1.33017388618892
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ScaleY
Vlow,VHigh,label
0 874 y
AxesVisible,ScaleVisible,Svaluevisible,ScaleGuidevisible
0 0 0 0
NUmber,Base,Linterval
1 1 1
High,Low
1.2493757047853 -1.20913343726815
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ScaleS
SquareQ AreaRectify PsMesh AxisWidth FontSize AxisOn letterCenterShowPOsition ShowEquation AxisType PolorNum Areafixed
1 1 0 3 32 0 0 0 0 0 12 0
----------
Yvalue
1 1
----------
Iinterval
Svalue Evalue sliceNo
1 -1
1 1
40
Dfuncno Efuncno AreaQ
1 0 0
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Yvalue Function List
9
y1
y2
y3
y4
y5
y6
y7
y8
y9
----------
Panel Position
0 0 0 0 548 0 0 0 0 0 0 0 1 0 1 0
1
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MEMO SECTION
Style, Color, BGcolor , Size, PositionX, positionY
3 0 0 14 0 0 0

43
An ellipse O(a, b) touches 
a circle O'(r) internally at 
two points, and a diameter 
AB of the circle touches 
the ellipse at an endpoint 
of its minor axis. 
The line tangent to the ellipse 
at the other endpoint of its 
minor axis meets the circle 
at P and Q. 

Show that AQ=2a. 
#//Set a at first Value
#a:=0.9
#draw

#//Set a at minmal Value
#a:=1/Sqrt(2)
#draw

#//Show
#On a change
#if a<1/Sqrt(2) then a:=1/Sqrt(2)
#if a>0.999 then a:=0.999
#k:=0
#Calc
#ClrAImg
#HideObj(L6,L4,U)
#Wait(500)
#ShowObj(L4,U)
#for k:=0 to 1 step 0.01
#draw
#next k
#Wait(800)
#ShowObj(L5,L6)
#Wait(300)
#HideObj(L5,L6)
#Wait(300)
#ShowObj(L5,L6)
#Wait(3000)
#HideObj(L4,L5,L6,U)
#Wait(1000)
#ClrAImg
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11
4 24 1
8 142 1
8 50 0
8 50 0
8 50 0
8 50 0
8 50 0
8 50 0
8 50 0
8 50 0
4 24 0
----------