Why is the coefficient of $r^2$ and $r$ equal to zero if a line lies wholly on a surface? (see pics)
2026-04-02 22:09:06.1775167746
Properties of a line lying wholly on a surface
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1
The result of plugging the parametrization of the line into the conicoid equation is a polynomial in $r$ which is identically equal to zero.
If a polynomial is identically equal to zero, then each of its coefficients is identically equal to zero.