曲線x^2-y^2=a^2與(x-1)^2+y^2=1恰好有三個公共點(diǎn)，則a為

熱心網(wǎng)友

曲線x^-y^=a^與(x-1)^+y^=r^恰好有三個公共點(diǎn)，則a為 解:曲線x^-y^=a^是等軸雙曲線方程,關(guān)于x軸,y軸對稱.它的左頂點(diǎn)Ａ1(a,0).曲線(x-1)^+y^=r^是圓方程,圓心坐標(biāo)是(1,0),半徑為r關(guān)于x軸對稱.要使二曲線恰好有三個公共點(diǎn),由曲線對稱性,圓與等軸雙曲線右邊相交兩個公共點(diǎn),左邊二曲線恰好切于等軸雙曲線左頂點(diǎn)Ａ1(a,0).∴r-1=a①r=2時,a=1②r=√2時,a=√2-1③r=1時,a=0.曲線x^-y^=0是兩條相交直線恰好也有三個公共點(diǎn).