Parabola

Geometry Level 3

A rectangle is completed with three of its vertices (with integer coordinates) are on the parabola \({y^2} = 4x\) and the normals at these points meet at a common point. If the area of the rectangle is 140 units and the fourth vertex is \((a,\,b)\)then find the value of \(\frac{{|a| + |b|}}{5}\).

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