Question

(理)方程xy²-x²y=-2所表示的曲線的對稱性是

A.關(guān)于原點(diǎn)對稱                        B.關(guān)于兩坐標(biāo)軸對稱

C.關(guān)于直線y=x對稱                    D.關(guān)于直線y=-x對稱

Answer 1

(理)解析:x換-x,得-xy²-x²y=-2,方程變化,曲線不關(guān)于y軸對稱;

y換-y，得xy²+x²y=-2，方程變化,曲線不關(guān)于x軸對稱;

x換-x,y換-y,得-xy²+x²y=-2,即xy²-x²y=2,方程變化,曲線不關(guān)于坐標(biāo)原點(diǎn)對稱;

x換-y,y換-x,得-yx²+y²x=-2,即xy²-x²y=-2,方程不變化,

∴曲線關(guān)于y=-x對稱.

答案:D