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The locus of the point $P$ which is equidistant from $3 x+4 y+5=0$ and $9 x+12 y+7=0$, is
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a straight line
Given lines are $3 x+4 y+5=0$ and $9 x+12 y+7=0$. Both lines are parallel. Hence, locus of the point $P$, which is equidistant from both lines, is a straight line which is an angular bisector.
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