JEE Main & Advanced Mathematics Straight Line Question Bank Problems related to triangle and quadrilateral Locus

  • question_answer
    Locus of the points which are at equal distance from \[3x+4y-11=0\]and \[12x+5y+2=0\]and which is near the origin is [MNR 1987]

    A)            \[21x-77y+153=0\]                   

    B)            \[99x+77y-133=0\]

    C)            \[7x-11y=19\]                           

    D)            None of these

    Correct Answer: B

    Solution :

               Let point be \[({{x}_{1}},{{y}_{1}}),\]then according to the condition \[\frac{3{{x}_{1}}+4{{y}_{1}}-11}{5}=-\left( \frac{12{{x}_{1}}+5{{y}_{1}}+2}{13} \right)\]                    Since the given lines are on opposite sides with respect to origin, hence the required locus is \[99x+77y-133=0\] .


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