question_answer

Tangents drawn from origin to the circle \[{{x}^{2}}+{{y}^{2}}-2ax-2by+{{b}^{2}}=0\]are perpendicular to each other, if   [MP PET 1995]

A)            \[a-b=1\]                                  

B)            \[a+b=1\]

C)            \[{{a}^{2}}={{b}^{2}}\] 

D)            \[{{a}^{2}}+{{b}^{2}}=1\]

Correct Answer: C

Solution :

           Obviously, tangents from origin will be perpendicular if it touches both axes i.e., \[a=b\] or \[{{a}^{2}}={{b}^{2}}\].