题型:解答题 题类:其他 难易度:难
设\({{F}_{1}},{{F}_{2}}\)分别是椭圆\(E:{{x}^{2}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1\left( 0 < b < 1 \right)\)的左、右焦点,过\({{F}_{1}}\)的直线\(l\)与\(E\)相交于\(A,B\)两点,且\(\left| A{{F}_{2}} \right|,\left| AB \right|,\left| B{{F}_{2}} \right|\)成等差数列.
\((1)\)求\(\left| AB \right|\);
\((2)\)若直线\(l\)的斜率为\(1\),求\(b\)的值.