Writing $$P$$ in terms of parametric co-ordinates $$2+r$$

$$\begin{aligned} & \cos \theta, 3+\mathrm{r} \sin \theta \text { as } \tan \theta=\sqrt{3} \\ & \mathrm{P}\left(2+\frac{\mathrm{r}}{2}, 3+\frac{\sqrt{3} \mathrm{r}}{2}\right) \end{aligned}$$

$$\mathrm{P}$$ must satisfy $$2 \mathrm{x}-3 \mathrm{y}+28=0$$

So, $$2\left(2+\frac{r}{2}\right)-3\left(3+\frac{\sqrt{3} \mathrm{r}}{2}\right)+28=0$$

We find $$r=4+6 \sqrt{3}$$