JEE Advance Conics

Geometry Level 5

From a variable point \(P~(t^2,2t),~1\leq t\leq 3\) on the parabola \(y^{2}=4x\), perpendicular \(PM\) is drawn to the tangent at the vertex. Now, from the mid point \(Q\) of \(PM\), perpendicular \(QL\) is drawn to the focal chord through \(P\). Find the sum of length of focal chord such that \(QL\) is maximum and maximum length of \(QL\)

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