### 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

**x**occur, the curve in symmetrical about

*if only even powers of*

**y - axis;***occur,*

**y**then the curve is symmetrical about

**x - axis.**If only even powers of

*and*

**x***both occur in the equation,*

**y**then the curve is symmetrical about both axes .

i.e. the curve

**(square of y)=4ax**is symmetrical about

*only;*

**y - axis**the curve

**square of x + square of y = square of a**is symmetrical about both axes.

Replace

*for*

**x***and*

**y***for*

**y**

**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.**
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