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AP EAMCET202420 May 2024Evening ShiftMathematicsStraight LinesActual

The circumcentre of the triangle formed by the lines x+y+2=0,2 x+y+8=0 and x-y-2=0 is

Options

  1. A(-5,1)
  2. B(-4,0)
  3. C(0,-2)
  4. D( -8 3 , -2 3 )

Correct answer

B. (-4,0)

Step-by-step solution

x+y+2=0 .... (i) aligned & 2 x+y+8=0 .... (ii) & x-y-2=0 .... (iii) aligned Solving (i) and (ii), we get (x, y)=(-6,4) Solving (i) and (iii). we get (x, y)=(0,-2) Solving (ii) and (iii), we get (x, y)=(-2,-4) Hence, vertices of triangles are (0,-2),(-6,4) , (-2,-4) Which is a right angled triangle, Ends of hypotenuse are (-6,4) and (-2,-4) So, circumcentre = mid-point of hypotenuse = ( -6-2 2 , 4-4 2 )=(-4,0)

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