Is the graph of 3x^2-2y^2=3 symmetric with respect to the x-axis,y-axis, and the origin

Question

graph of 3x^2-2y^2=3

Answer 1

This is an rectangular hyperbola, so it is symmetric about x-axis , y-axis and origin.

Symmetric about y-axis if f(x,y) = f(-x,y)

3x^2-2y^2=3 <=> 3(-x)^2-2y^2=3

Symmetric about x-axis,  if f(x,y) = f(x,-y)

3x^2-2y^2=3 <=> 3(x)^2-2(-y)^2=3

Symmetric about origin, if f(x,y) = f(-x,-y)

3x^2-2y^2=3 <=> 3(-x)^2-2(-y)^2=3