If the radius of the largest circle with centre (2,0)  inscribed in the ellipse$x^2+4y^2=36$  is r then12r²   is

The equation of normal at $\mathrm{\theta }$  to an  

ellipse is $\frac{6\mathrm{x}}{\cos \mathrm{\theta }}-\frac{3\mathrm{y}}{\sin \mathrm{\theta }}=27$
$\begin{array}{l}\mathrm{If} \mathrm{it} \mathrm{passes} \mathrm{through} \mathrm{centre} \mathrm{of} \mathrm{circle} (2,0)\Rightarrow \frac{12}{\cos \mathrm{\theta }}=27\\ \Rightarrow \cos \mathrm{\theta }=\frac{4}{9} \\ \text{ then }\mathrm{r}=\mathrm{CP}=\sqrt{\frac{23}{3}}\\ \therefore 12{\mathrm{r}}^2=92\end{array}$