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 \[99x+77y-133=0\] .

"> 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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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]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) . 8 months ago

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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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