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1,4 . 155,180.
. . 5, : 2,3, 4. . 84, 365-372, . 86 375-387.
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1.
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: - F d. AD , , , , , FAD
1. - .
FA=FD FAD .
2. , A AFD. FD.
3. ' FD', : A'F=A'D.
4. , A' : A'F A'D'.
A'F=A'D>A'D' , ( ) - .
: , FAD FAK=DAK. DAK () = , FAK= . :
, , , . , (FAD)= .
2.
: - F1 F2, , , , F1AF2.AF1+AF2=2C; F':AF'=AF; a - F2AF'.
1. F2AF1 , - F2F'.
2.A' , - , : A'F2=A'F'.
3. , A' . A'F1+A'F2=A'F1+ A'F'>F1F'=2C, A' , . , .
: 1=2 .. - , 2=3, , 1=3. : , , , (3- , 1- )
3.
, , , , .
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: , .
, , (;) (k = /x)
: -= /x (x-xo); 0, /x f,().
y-yo=f,(xo)(x-xo)
=F(y) x-xo=F,(yo)(y-yo)
1..
2=2px
X=y2/2px
Xy=y
X(y0)=y0/p
x-x0=y0/p(y-y0)
px-px0=y0y-y02(1)
y02=2px:
px+px0=y0y
y0y=p(x+x0)
2..
x2/a2=y2/b2=1
(x-xo)
, y0 0
y:
Y=bÖ1-x2/a2
Y=b1/Ö1-x2/a2* (-2x/a2)
Y(x0)= -bx0/a2Ö1-x2/a2= bx20/a2bÖ1-x2/a2*(-2x/a2)
Y - y0=-b2x0/ a2y0(x-x0)
xx0/a2 + yy0/b2=1
: , , , .. , (x0,y0) .
: :
xx0/a2 - yy0/b2=1.
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A, B C . (1)
ax 2 + by 2 + c = 0
px 2 + qy = 0.
(1) B 2 AC, B 2 = AC. , , . , q 0, . .
1) a, b c , , . ( , a = b).
2) a b , c , ; a = b .
3) a b , .
4) a b c = 0, .
5) a b c = 0, , , . , a = b, .
6) a, b , , .
7) a, b , , , . , .
8) c = 0, a, b , . ( a = b = 0, (1) .)
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9) , p q . p 0, q = 0, . 8. p = 0, , (1) .
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, , .. , f (x, y, z) = 0. -, , , z 2 = x 2 + y 2. ABCD V. FDC VB F, CD DFPC, P . CD E EF AB. P , , RPS EF Q. QF QP , , x y P. .
. , , .
y 2 = RQ X QS.
RQ ( P AE), QS x ( QS / EB = QF / FE). ,
a . a .
, RQ AE; y 2 = RQ QS
a b , , ,
. x (x = a x = a) y (y = b y = b) . , , :
, ,
x, x 2 = a 2, , y, y 2 = b 2, . a b (4a) , .
xy = k.