co ordinate geo

Asked by kirtichawla94 | 8th Dec, 2009, 06:52: PM

Expert Answer:

  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)

 

 

Answered by  | 11th Dec, 2009, 10:50: AM

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