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Q. $\displaystyle\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{\pi / 2-\theta}{\cot \theta}=$

KCETKCET 2022

Solution:

Center $\&$ radius of given circle are $C(1,1) \& r=1$.
Required locus is a circle with $C (1,1) \& r =1+4=5$.
$\therefore$ Its equation is $(x-1)^{2}+(y-1)^{2}=5^{2}$
$ \Rightarrow x^{2}+y^{2}-2 x-2 y-23=0$.