Differentiation - Tangents and Normals at a Point

A curve is such that \(\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{9}{5\sqrt{2x+7}}\) and \(P\left(1, \frac{1}{3}\right)\) is a point on the curve. The normal to the curve at \(P\) meets the \(x\)-axis at \(Q\) and meets the \(y\)-axis at \(R\).

1. Find the coordinates of \(R\) and of \(Q\).
2. Find the equation of the curve.