JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Critical Thinking

  • question_answer
    The circumcentre of the triangle formed by the lines \[xy+2x+2y+4=0\] and \[x+y+2=0\]              [EAMCET 1994]

    A)            (0, 0)                                        

    B)            (-2, - 2)

    C)            (-1, -1)                                    

    D)            (-1, -2)

    Correct Answer: C

    Solution :

               The separate equations of the lines given by \[xy+2x+2y+4=0\] are \[(x+2)(y+2)=0\] or \[x+2=0\], \[y+2=0\]. Solving the equations of the sides of the triangle, we obtain the coordinates of the vertices as \[A(-2,0),\ B(0,-2)\]and \[C(-2,-2)\]. Clearly, \[\Delta ABC\]is a right angled triangle with right angle at C. Therefore the centre of the circum-circle is the midpoint of AB whose coordinates are (-1, -1).

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