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of the 2 × 2 matrix) and the quantity (the trace of the 2 × 2 matrix) are invariant under arbitrary rotations and translations of the coordinate axes, as is the determinant of the 3 × 3 matrix above. The constant term and the sum are invariant under rotation only.

Eccentricity in terms of coefficients

When the conic section is written algebraically as

:

the eccentricity can be written as a function of the coefficients of the quadratic equation. If the

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