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Three normals with slopes m1, m2 and m3 ...

Three normals with slopes `m_1, m_2 and m_3` are drawn from a point P not on the axis of the parabola `y^2 = 4x`. If `m_1 m_2` = `alpha`, results in the locus of P being a part of parabola, Find the value of `alpha`

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