數學高手唔該幫幫我！

The words ' smaller circle ' suggests that the required circle C' touches C: x2 + y2 - 2x + 4y - 11 = 0 internally.
Centre of C: ( 1, -2 ) and radius of C:
0.5 [ (-2)2 + 42 - 4(-11) ]0.5 = 4
Thus, the end - point of C is ( 1 , 2 ).
=> radius of C' = 2 - 1 = 1
Hence equation of C' : ( x - 1 )2 + ( y - 1 )2 = 1
x2 + y2 - 2x - 2y + 1 = 0