Straight lines, circles and now parabola, It always forms a sequence

Geometry Level pending

A circle touches the parabola \(y^{2}=4ax\) , at P. It also passes through focus S of parabola and intersects its axis at Q. The angle SPQ is 90 degrees .Then the equation of circle is \(A( x )^{2} + B(y)^{2} + Ca(x)+Da(y)+ E(a)^2=0\).

Find the value of \(A+B+C+D+E\) + ( Sum of numbers from 1 to 100 that are divisible by 2 or 5 )

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