Parabola

Geometry Level 3

A rectangle is completed with three of its vertices (with integer coordinates) are on the parabola y 2 = 4 x {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 ) (a,\,b) then find the value of a + b 5 \frac{{|a| + |b|}}{5} .

6 8 4 3

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