X,y)\] is the curve\[|x|+|y|=1\]. If the point lies in the first quadrant, then \[x>0,y>0\] and so \[|x|+|y|=1\Rightarrow x+y=1\], which is straight line AB. If the point \[(x,\,y)\]lies in second quadrant then \[x<0\], \[y>0\] and so \[|x|+|y|=1\] Þ \[-x+y=1\] Similarly for third and fourth quadrant, the EQUATIONS are \[-x-y=1\]and \[x-y=1\].                    Hence the required locus is the curve consisting of the SIDES of the SQUARE ABCD.

"> X,y)\] is the curve\[|x|+|y|=1\]. If the point lies in the first quadrant, then \[x>0,y>0\] and so \[|x|+|y|=1\Rightarrow x+y=1\], which is straight line AB. If the point \[(x,\,y)\]lies in second quadrant then \[x<0\], \[y>0\] and so \[|x|+|y|=1\] Þ \[-x+y=1\] Similarly for third and fourth quadrant, the EQUATIONS are \[-x-y=1\]and \[x-y=1\].                    Hence the required locus is the curve consisting of the SIDES of the SQUARE ABCD.

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If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is [IIT 1992, Karnataka CET 1999; DCE 2000,01]

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

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Required locus of the point \[(X,y)\] is the curve\[|x|+|y|=1\]. If the point lies in the first quadrant, then \[x>0,y>0\] and so \[|x|+|y|=1\Rightarrow x+y=1\], which is straight line AB. If the point \[(x,\,y)\]lies in second quadrant then \[x<0\], \[y>0\] and so \[|x|+|y|=1\] Þ \[-x+y=1\] Similarly for third and fourth quadrant, the EQUATIONS are \[-x-y=1\]and \[x-y=1\].                    Hence the required locus is the curve consisting of the SIDES of the SQUARE ABCD.

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Posted on 14 Sep 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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