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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