Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 46 стр.

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det A det
e
A
` A
n
v
M
0
x
i
= x
i
0
+ tv
i
Φ
a
ij
(x
i
0
+ tv
i
)(x
j
0
+ tv
j
) + 2a
i n+1
(x
i
0
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i
) + a
n+1 n+1
= 0
(a
ij
v
i
v
j
)t
2
+ 2t(a
ij
x
j
0
v
i
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i n+1
v
i
) + F (x
k
0
) = 0
t
F
i
(x
k
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)v
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F
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k
) = 2(a
ij
x
j
+ a
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i
ϕ(v)t
2
+ F
i
(x
k
0
)v
i
t + F (x
k
0
) = 0.
v
ϕ ϕ(v) = 0 `
Φ v
ϕ
a
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v
i
v
j
= 0
`
t
1
t
2
` Φ M
1
M
2
A
C
n
( ) M
1
M
2
Φ
M
1
M
2
t
t
1
+ t
2
2
M
0
(x
i
0
)
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                 (aij v i v j )t2 + 2t(aij xj0 v i + ai n+1 v i ) + F (xk0 ) = 0
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                          ϕ(v)t2 + Fi (xk0 )v i t + F (xk0 ) = 0.              •¶Š‹
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