alleryStart learning →What stays unchanged when the axes are rotated to remove the xy term?
AThe coefficient B of the xy term
BThe constant term F of the conic
CThe discriminant B squared minus 4AC
DThe sum of A and C squared
Answer & Solution
Correct answer: C. The discriminant B squared minus 4AC
1. Rotating the axes rewrites every coefficient of the general form.
2. One combination survives the rewrite untouched, and it is called invariant.
3. That combination is the discriminant, B squared minus 4AC.
4. The coefficient B cannot be the invariant, since the whole point of rotating is to drive it to zero.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.4 Rotation of Axes_
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