question_answer

If the two circles \[{{(x-1)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}-8x+2y+8=0\] intersect in two distinct points, then     AIEEE  Solved  Paper-2003

A) \[2<r<8\]                            

B) \[r<2\]                 

C)       \[r=2\]                 

D)       \[r>2\]

Correct Answer: A

Solution :

Two circles of radii  and  respectively intersect  in  two  distinct  points,   if             . The equation of first circle is                     Centre  (1, 3) and radius and equation of second circle is                     Centre (4, - 1) and radius                                                             Two circles intersect in two distinct points, then                                                                                                                             and                                       and