Let the parabola \(y={x}^{2}+px+q\) passing through the point \((1,-1)\) be such that the distance between its vertex an…

Let the parabola \(y={x}^{2}+px+q\) passing through the point \((1,-1)\) be such that the distance between its vertex and the \(x-\)axis is minimum. Then the value of \({p}^{2}+{q}^{2}\) is:

[JEE Main 2026, 2 Apr (Shift 2)]