<Qua-2025-782>, hint

 Let vectors OA, OB be a, b and OM=tb+(1-t)a, ON=-xa, OP=-yb

Line MO cuts PN in M', midpoint of NP.

Since MO/OM'=2/1, PM'=NM'

1/2(-) OM =-xa-yb  ..> 1/2 {tb+(1-t)a}=xa+yb,  Then y=t/2 x(1-t)/2

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