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Number of points of intersection of the curve |y|=|ln|x|| with the curve |y-2|=|x| is

Number of points of intersection of the curve |y|=|ln|x|| with the curve |y-2|=|x| is

Grade:11

2 Answers

Aditya Gupta
2081 Points
4 years ago
hello ananya, this ques can be done by drawing the graphs of both the functions and noting the number of intersections.
obviously for |y|=|ln|x|| we only need to draw the graph in the first quadrant (where both x and y are positive), and that graph can then be reflected across the x and y axes to obtain the complete graph in all four quads. similarly, |y-2|=|x| needs to be drawn only for first and fourth quads as x is positive there and that graph can then be reflected about the y axis. the reasons for all of these simplifications is that in the first relation, replacing y by – y and/or x by – x doesnt change the relation. similarly for the second relation, changing x by – x keeps it the same (although changing y by – y doesnt).
taking these into consideration, we can draw graphs and note that Number of points of intersection is 6.
kindly approve :)
Samyak Jain
333 Points
4 years ago
I appreciate you have explained it properly but the final answer is wrong.
There are 4 points of intersection in the first and fourth quadrants and other 4 in the second and third quadrants.
In this way, the number of points of intersection of the given curves is 8.

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