question_answer

The largest value of r for which the region represented by the set\[\{\omega \in C/|\omega -4-i|\le r\}\]is contained in the region represented by the set \[\{z\in C/|z-1|\le |z+i|\},\]is equal to : JEE Main Online Paper (Held On 10 April 2015)

A) \[2\sqrt{2}\]                                      

B) \[\sqrt{17}\]

C) \[\frac{5}{2}\sqrt{2}\]                   

D) \[\frac{3}{2}\sqrt{2}\]

Correct Answer: C

Solution :

                 Radius \[CP=\frac{4+1}{\sqrt{2}}\]                         \[=\frac{5}{\sqrt{2}}=\frac{5}{2}\sqrt{2}\] \[=\frac{dx}{{{\left( x-2 \right)}^{2}}}=-\frac{dt}{3}\] \[=\frac{-1}{3}\int_{{}}^{{}}{\frac{dt}{{{t}^{3/4}}}}=-\frac{1}{3}\int_{{}}^{{}}{t\frac{-3}{4}lt}\] \[=\frac{1}{3}\left[ \frac{{{t}^{\frac{-3}{4}+1}}}{\frac{-3}{4}+1} \right]\]\[=\frac{-4}{3}{{\left[ \frac{x+1}{x-2} \right]}^{1/4}}+c\]