Question

Given any two conics C1 and C2 , at least one element of R× R will belong to
C1 ∩C2.
Is the statement true? Give reason for your answers either with a
short proof or a counterexample.

Answer 1

Answer on Question #78761 – Math – Analytic Geometry

Question

Given any two conics $C_1$ and $C_2$, at least one element of $R \times R$ will belong to $C_1 \cap C_2$. Is the statement true? Give reason for your answers either with a short proof or a counterexample.

Answer

The statement is false. For example, if two planes intersecting cone are parallel then the given statement is false.

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