2024 IGCSE Additional Mathematics October/November 0606/12 Q8

The tangent to the curve \(y=\mathrm{e}^x(2x+5)^{\frac12}\) at the point where \(x=2\) meets the \(x\)-axis at the point \(X\) and the \(y\)-axis at the point \(Y\). Find the coordinates of the mid-point of \(XY\), giving your answer in exact form.[8]