A Curve and Two Lines

Geometry Level pending

Suppose \(g\) is the quadratic function with leading coefficient 1 whose graph is tangent to the lines \(5x+y-6=0\) and \(x-y-1=0\). The sum of the coefficients of \(g\) is \(\frac{p}{q}\), where \(p\) and \(q\) are positive coprime integers. Find the value of \(100p+q\).

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