Pencil of conics and periodic orbits

Let $\dot{x}=P(x,y)$ and $\dot{y}=Q(x,y)$ be a quadratic polynomial differential equation. Prove that if the pencil of conics $P+\lambda Q$ contains an imaginary conic, a real conic reduced to a single point, or a double straight line, then the system has no periodic orbits.

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