Ax2+Bxy+Cy2+Dx+Ey+F=0
B=0, - .
- :
×
,×˃0, ;
×˂0, ;
×=0, .
:
,
:
; .
1) ×˃0, . :
- .
- .
, - .
2) ×˂0, . :
, :
- .
:
- ( )
3):
=0, . :
.: :
- .
=0, - . :
.: - :
- .
.
,
F 1 (;0) F 2 (-;0), , = 2.
,
. a > b
, a < b
Y, a = b .
, .
F 1 F 2 = 2 , ,
. AB = 2 a ,
CD = 2 b . = c / a, e < 1
.
= .
: + =1, b=
. (x;y) -- . F1M+F2M=2a.
F1(-c;0),F2(c;0).
, b2=a2-c2, x2b2+y2a2=a2b2
, a2b2, + =1
.
x=A-1B= = =
∆ ∆ ∆
.
,
F (),
, = - ,
.
: y 2 = 2 p x.
.
F l p.
y2=2px
.
F(), x= .
M(x;y) -- .
M l MK,
|
|
M. MK= x+ .
MK=FM,
→ →
y2=2px
.
: Ax+By+Cz+D=0
(x )
A(x
Ax+By+Cz=A
Ax+By+Cz+D=0
1. D=0, - Ax+By+Cz=0 .
2. =0, By+Cz+D=0→ .
3. =0 D=0, By+Cz=0→ .
4. =0 =0, Cz+D=0→ XOy.
5. =0,=0,D=0, XOy.
:
( a;0;0) ( 0;b;0 ) (0;0;c)
Ax+By+Cz+D=0
Aa+D=0 Bb+D=0 Cc+D=0
a= b= c=
.
1. 2
.
ad-cb= - (cb- ad)
2., 2 , =0
ab-ab=0
3. 0 , =0.
4.
, , .
.
kad-kbc=k(ad-bc)
k(ad-bc)=k(ad-bc)
5. ,
2 . 1 1 ,
2 2.
=
(a+p)d-(b+s)c=ad-bc+pd-cs
ad+pd-bc-cs=ad-bc+pd-cs
6. . ,
, .
ad+kcd-bc-kcd=ad-bc
ad-bc=ad-bc
7..:
.
8. -
=0
9. 2
.
.