Symmetry Tests for Polar Graphs

[BigNate]

Hello Everyone,

I'm trying to better understand the concept here. Is there a time when either of the following are possible:
[a] There is symmetry about x-axis as well as symmetry about y-axis but no symmetry about the origin
There is no symmetry about the x-axis and no symmetry about the y-axis but there is symmetry about the origin

Thanks in advance for your time and knowledge!

 

[SAQLAIN AHMAD]

Hello Everyone,

I'm trying to better understand the concept here. Is there a time when either of the following are possible:
[a] There is symmetry about x-axis as well as symmetry about y-axis but no symmetry about the origin
There is no symmetry about the x-axis and no symmetry about the y-axis but there is symmetry about the origin

Thanks in advance for your time and knowledge!

Symmetry about y axis mean function is an even function and symmetry about origin means function is odd function.

[a] Ellipse is the best example whose equation is f(x,y)=(x^2/a^2)+(y^2/b^2)-1.f(x,y)=f(x,-y)&f(x,y)=f(-x,y).So symmetrical about both x- and y-axis but not about origin
Any odd function would do like x^3,sinx,etc