Tangential to Parabola

Algebra Level 2

Let \(y=x^2+px+q\) be the equation of a parabola tangential to the line \(y=14x.\) The locus of the vertex of this parabola for the changes in the values of \(p\) and \(q\) can be expressed as the equation \(y=ax+b.\) What is the value of \(a+b?\)

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