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MHT CET202522 Apr 2025Evening ShiftMathematicsStraight LinesActual

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

Options

  1. A2 units
  2. B1 unit
  3. C2 units
  4. D3 units

Correct answer

C. 2 units

Step-by-step solution

The given equations of the lines are: xy + 2x + 2y + 4 = 0 x + y + 2 = 0 Factor by grouping the first equation: x(y + 2) + 2(y + 2) = 0 (x + 2)(y + 2) = 0 This represents two perpendicular lines: x = -2 and y = -2 . The triangle is formed by the intersection of these lines with x + y + 2 = 0 . Finding the vertices from pairwise intersections: Vertex A: (-2, 0) from x = -2 and x + y + 2 = 0 Vertex B: (0, -2) from y = -2 and x + y + 2 = 0 Vertex C: (-2, -2) from x = -2 and y = -2 The side lengths are: AB = (0 - (-2))

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