英语翻译
∴$left{begin{array}{l}{1-2{k}^{2}≠0}{△={16k}^{2}+16({1-2k}^{2})=16(1-{k}^{2});>0}end{array}right.$
解得:-1<k<1且k≠±$frac{sqrt{2}}{2}$.
(2)设A(x1,y1),B(x2,y2),则x1+x2=$frac{4k}{1-2k^{2}}$
设P为AB中点,则P($frac{x_{1}+x_{2}}{2}$,$frac{k(x_{1}+x_{2})}{2}$+1),即P($frac{2k}{1-2k^{2}}$,$frac{1}{1-2k^{2}}$),
∵M(3,0)到A、B两点的距离相等,
∴MP⊥AB,∴KMP•KAB=-1,
即k•$frac{frac{1}{{1-2k}^{2}}}{frac{2k}{{1-2k}^{2}}-3}$=-1,解得k=$frac{1}{2}$,或k=-1(舍去),
∴k=$frac{1}{2}$.
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