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how to chect weather a given curve is symmetric about any given line
The two sides of a graph of curve, on either side of the axis of symmetry look like mirror images of each other. Tests for Symmetry : When you are graphing a relation given by an equation it is helpful to find out first whether its graph has any symmetries. The most common symmetries to look for are symmetry with respect to the x and y axes and the origin: 1) A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with -y. 2) A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with -x. 3) A graph will have symmetry about the origin if we get an equivalent equation when all the y’s are replaced with -y and all the x’s are replaced with -x ---- Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
The two sides of a graph of curve, on either side of the axis of symmetry look like mirror images of each other.
Tests for Symmetry : When you are graphing a relation given by an equation it is helpful to find out first whether its graph has any symmetries. The most common symmetries to look for are symmetry with respect to the x and y axes and the origin: 1) A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with -y. 2) A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with -x. 3) A graph will have symmetry about the origin if we get an equivalent equation when all the y’s are replaced with -y and all the x’s are replaced with -x
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Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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