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NHN DNG MT BC 2
Nhn dng mt bc 2Phng trnh tng qut ca mt bc 2:Ax2 + By2 + Cz2 + 2Dxy + 2Exz + 2Fyz + ax + by + cz + d = 0trong t nht 1 s hng bc 2 phi khc 0.
Phng trnh chnh tc ca mt bc 2EllipsoidMt cuHyperboloid 1 tng.Hyperboloid 2 tng.
Nn(Dng thng gp ca nn)Paraboloid ellipticParaboloid hyperbolic
Tr ellipticTr hyperbolicTr parabolic2 bin
Hnh nh cc mt c bnxzyEllipsoid
Mt cu
Hyperboloidzz
Nn
V nn
V nn
Paraboloid elliptic
V paraboloid elliptic
V paraboloid elliptic
Parapoloid hyperbolic
Tr ellipticCch v cc mt tr:V ng chun ( l ng cong bc 2 trong phng trnh mt)Cho ng bc 2 di chuyn dc theo trc khng cha bin xut hin trong phng trnh mt
V tr
V tr
Tr hyperbolic
Tr parabolic
a dng ton phng trong phng trnh tng qut v chnh tc. Kh cc s hng bc nht (nu c s hng bc 2 i chung) a pt v dng chnh tc v nhn dng.Trong chng trnh ch v nhng mt chnh tc.Cch phn loi mt bc 2:
V d
V dTm pt chnh tc v phn loi cc mt bc 2:a dng ton phng (cc s hng bc 2) v dng chnh tc bng php bin i trc giao:(1)
Php bin i
Phng trnh (1) vit liParaboloid hyperbolic-16-16-8
a dng ton phng v chnh tcPhp bin i:(2)
Phng trnh (2) vit liElippsoid
Dng php bin i LagrangeParapoloid hyperbolic
Cc mt phng song song cc mt ta y = az = ax = axxxyyyzzz
Mt s mt phngzxx + z = 1
Mt s mt phngzy = x
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