<s>[INST] projection of $x^2+y^2+z^2-yz=1$ to xoy plane if the surface is projected to yoz plane, I known than the equation of the projection is $y^2+z^2-yz-1=0$. But what what about xoy plane,  is the equation of project projection  $x^2+y^2=1$?
 [/INST] $$
x^2+y^2+z^2-yz=1
\\
z^2-yz+\left( x^2+y^2-1 \right) =0
\\
\Delta =-4x^2-3y^2+4\ge 0
\\
x^2+\frac{3}{4}y^2\le 1
$$
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