CBSE Class 10 Answered

  Let the coordinates of the centre be (x,y) and r be the radius.

  Then from diatance formula,

  For point (1,2):

  (x-1)² + (y-2)² = r²

  i.e x² + y² - 2x - 4y + 5 = r²  .............(1)
 

   For point (3,-4):
  (x-3)² + (y + 4)² = r²

  i.e x² + y² - 6x  + 8y + 25 = r²  .............(2)

   For point (5,-6):
  (x-5)² + (y + 6)² = r²

  i.e x² + y² - 10x  + 12y + 61 = r²  .............(3)

Now subtracting (2) from (1) gives,

   x - 3y = 5 ..............(4)

Now subtracting (3) from (2) gives,

   x - y = 9 ..............(5)

On solving equation (4) and (5), we get

  y = 2 and x =11

So, the coordinates of the centre is (11,2)