[線代] Quadratic curve
In |R^3, let C be a circle lying on a plane P which does not pass through
the origin (0,0,0). Let
Γ={(x,y)∈|R^2｜(tx,ty,t)∈C for some t∈|R}
Show that Γ is a quadratic curve. Namely, there is a polynomail F(X,Y) of
total degree 2 such that
Γ={(x,y)∈|R^2｜F(x,y)=0}
Is Γ is ellipse, a parabola or a hyperbola?
感謝大家給與想法
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