NH N D NG M T B C 2Ậ Ạ Ặ Ậ
Nh n d ng m t b c 2ậ ạ ặ ậ
Ph ng trình t ng quát c a m t b c 2:ươ ổ ủ ặ ậ
Ax2 + By2 + Cz2 + 2Dxy + 2Exz + 2Fyz
+ ax + by + cz + d = 0
trong đó ít nh t 1 s h ng b c 2 ph i khác 0.ấ ố ạ ậ ả
Ph ng trình chính t c c a m t b c 2ươ ắ ủ ặ ậ
2 2 2
2 2 2
1
x y z
a b c
+ + =
2 2 2 2
x y z R+ + =
2 2 2
2 2 2
1
x y z
a b c
+ − = −
2 2 2
2 2 2
1
x y z
a b c
+ − =
Ellipsoid
M t c uặ ầ
Hyperboloid 1 t ng.ầ
Hyperboloid 2 t ng.ầ
( )
+ + +
( )
, 0C+ + −
2 2 2
2 2 2
0
x y z
a b c
+ − =
Nón
2 2
2
2 2
x y
za b
= +
(D ng th ng g p c a nón)ạ ườ ặ ủ
2 2
2 2
x y
cz d a b
+ = +
2 2
2 2
x y
cz d a b
+ = −
Paraboloid elliptic
Paraboloid hyperbolic
( )
, 0C+ + − =
( )
+ +
( )
+ −
2
2y px=
2 2
2 2 1
x y
a b
+ =
2 2
2 2 1
x y
a b
− =
Tr ellipticụ
Tr hyperbolicụ
Tr parabolicụ
2 bi nế