题目

  Droughts (干旱)are common in Kenya . Before ,they came every 10 years ,but now they seem to be hitting us more often and for a longer time .   We gave the droughts names :“longoza”was the drought when many animals died ; there was the drought of the “planes” because food was dropped from the air by planes; and one particularly bad drought was called “ man who dies with his money in his fist (拳头)”，because ,even if there was money , there was simply no food to buy .  I was born in 1951 in Machakos. From what my mother tells me , when I was 7, there was a serious dr9．已知椭圆$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1（a＞b＞0）右顶点与右焦点的距离为$\sqrt{3}$-1，短轴长为2$\sqrt{2}$．（Ⅰ）求椭圆的方程；（Ⅱ）过左焦点F的直线与椭圆分别交于A、B两点，若△OAB（O为直角坐标原点）的面积为$\frac{3\sqrt{2}}{4}$，求直线AB的方程．