The point \(S\) is a focus of the ellipse \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\), and \(P\) is a point on the ellipse such that \(PS\) is perpendicular to the axis of \(x\). The tangent and normal to the ellipse at \(P\) meet the axis of \(y\) in \(Q\) and \(R\) respectively. If \(H\) is the other focus of the ellipse prove that \(QR=HP\).