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Normals at (x(1),y(1)),(x(2),y(2))and(x(...

Normals at `(x_(1),y_(1)),(x_(2),y_(2))and(x_(3),y_(3))` to the parabola `y^(2)=4x` are concurrent at point P. If `y_(1)y_(2)+y_(2)y_(3)+y_(3)y_(1)=x_(1)x_(2)x_(3)`, then locus of point P is part of parabola, length of whose latus rectum is __________.

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