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Figure 9.6.4

EXAMPLE 7 Eliminating the Cross-Product Term Plus Translation                   (9)
Describe the conic C whose equation is                                         (10)

Solution

The matrix form of this equation is

where
As shown in Example 6,

orthogonally diagonalizes A and has determinant 1. Substituting  into 9 gives
or

Since

10 can be written as
   722   723   724   725   726   727   728   729   730   731   732