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Let PQ be a variable normal chord of the...

Let PQ be a variable normal chord of the parabola `y^2 = 4x` whose focus is `S`. lf the locus of the centroid of the triangle `SPQ` is the curve `gy^2 (3x-5) = ky^4 + w` where `g, k, w, in N`, find the least value of `(g+k+w)`

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