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Wednesday, 9 April 2014

Symmetry of Curve

 


Symmetry of Curve about axes or any line :-

Following are the process of judge the symmetry of curve :-

If in the equation of a curve only even powers of   

occur, the curve in symmetrical about

y - axis;   if only even powers of    occur,

then the curve is symmetrical about   x - axis.

If only even powers of  and    both occur in the equation,

then the curve is symmetrical about both axes .

i.e. the curve   (square of  y)=4ax

is symmetrical about  y - axis only;

the curve  square of  x + square of  y = square of  a

is symmetrical about both axes.

Replace   for  y  and  y   for  x,

and if there is no change in equation,

the curve is symmetrical about the line

y=x.

For example; the rectangular hyperbola given by

xy=square of  c 

is symmetrical about the line    y=x.