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The equation of the circle circumscribing the triangle formed by the lines x + y = 6 ,   2 x + y = 4 and x + 2 y = 5 is

Options

  1. Ax 2   +   y 2 +   17 x   +   19 y   -   50   =   0
  2. Bx 2   +   y 2   -   17 x   -   19 y   -   50   =   0
  3. Cx 2   +   y 2   +   17 x   -   19 y   -   50   =   0
  4. Dx 2   +   y 2   -   17 x   +   19 y   +   50   =   0

Correct answer

D. x 2   +   y 2   -   17 x   +   19 y   +   50   =   0

Step-by-step solution

Let the triangle thus formed is △ A B C , where A B :   x + y = 6 , B C :   2 x + y = 4 and C A :   x + 2 y = 5 Now we can find coordinates of point A , B and C by solving these three eqautions. Solving A B and B C , we get B - 2 , 8 . Similarly we get, A 7 , - 1 and C 1 , 2 . Now let the equation of circle passing through vertices of △ A B C is x 2 + y 2 + 2 g x + 2 f y + c = 0 Now, point A ,   B   a n d   C will satisfy this general equation. x 2 + y 2 + 2 g x + 2 f y + c

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