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Consider a variable line L which passes ...

Consider a variable line `L` which passes through the point of intersection `P` of the line `3x+4y- 12=0` and `x + 2y-5=0` meeting the coordinate axes at points `A` and `B : (1)`Locus 8f the middle point of segment `AB` has the equation: `(2)`Locus of the feet of the perpendicular from the origin on the variable `L` has the equation `(3)` Locus of the centroid of the variable triangle `OAB` has the equation (where `O` is the origin)

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