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MHT CET202526 Apr 2025Morning ShiftMathematicsStraight LinesActual

The circumcenter of the triangle formed by lines x y +2 x+2 y +4=0 and x+ y +2=0 is

Options

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

Correct answer

C. (-1,-1)

Step-by-step solution

The given equation xy + 2x + 2y + 4 = 0 factors into (x + 2)(y + 2) = 0 , yielding the lines x = -2 and y = -2 . A third line is given as x + y + 2 = 0 . Find the vertices of the triangle: Intersection of x = -2 and y = -2 is (-2, -2) . Intersection of x = -2 and x + y + 2 = 0 gives y = 0 , vertex (-2, 0) . Intersection of y = -2 and x + y + 2 = 0 gives x = 0 , vertex (0, -2) . With vertices at (-2, -2) , (-2, 0) , and (0, -2) , the triangle is right-angled at (-2, -2) . The hypotenuse is between (-2, 0) and (0, -2

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