QJEEM24Ma94a8: JEE Main 2024 Mathematics - Class 11 JEEM24Ma94a8 Solution: The distance of the point from the line , measured parallel to…

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