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
y - axis; if only even powers of y occur,
then the curve is symmetrical about x - axis.
If only even powers of x and y 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 x for y and y for x,
and if there is no change in equation,
the curve is symmetrical about the line
For example; the rectangular hyperbola given by
xy=square of c
is symmetrical about the line y=x.