Answer
(a) symmetric with respect to the x-axis.
(b) symmetric with respect to the y-axis.
(c) symmetric with respect to the origin.
Work Step by Step
(a) To test symmetry with respect to the x-axis, replace $(x,y)$ with $(x,-y)$, we have $3(x)^2-2(-y)^2=3\longrightarrow 3(x)^2-2(y)^2=3$ which is the same as the original equation, thus the graph is symmetric with respect to the x-axis.
(b) To test symmetry with respect to the y-axis, replace $(x,y)$ with $(-x,y)$, we have $3(-x)^2-2(y)^2=3\longrightarrow 3(x)^2-2(y)^2=3$ which is the same as the original equation, thus the graph is symmetric with respect to the y-axis.
(c) To test symmetry with respect to the origin, replace $(x,y)$ with $(-x,-y)$, we have $3(-x)^2-2(-y)^2=3\longrightarrow 3(x)^2-2(y)^2=3$ which is the same as the original equation, thus the graph is symmetric with respect to the origin.
