\(P_{o}\) is the parabola \(y^{2}=4x\) with vertex \(K(0,0)\), \(A\) and \(B\) are points on \(P_{o}\) where tangents are at right angles. Let \(C\) be the centroid of \(\Delta ABK\). The locus of \(C\) is another parabola \(P_{1}\). Now the process is repeated with \(P_{1}\) then \(P_{2},P_{3}....\) etc. Then the length of latus rectum of \(P_{10}\) can be expressed as \(\frac{a}{b}\) where \(a,b\) are co prime natural numbers.

Find \(a+b\) .

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