Given three points on the \( x y \) plane on \( O(0,0), A(1,0) \) and \( B(-1,0) \). Point \( P ...

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Given three points on the \( x y \) plane on \( O(0,0), A(1,0) \) and \( B(-1,0) \). Point \( P \) is moving on the plane satisfying the condition \( (\overrightarrow{P A} \cdot \overrightarrow{P B})+3(\overrightarrow{O A} \cdot \overrightarrow{O B})=0 \).
If the maximum and minimum values of \( |\overrightarrow{P A}| \cdot|\overrightarrow{P B}| \) are \( M \) and \( m \) respectively then find the value of \( M^{2}+m^{2} \).
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