过双曲线x2/3-y2/6=1右焦点F2,且倾斜角为π/6的直线交双曲线于AB两点,求△F1AB面积
问题描述:
过双曲线x2/3-y2/6=1右焦点F2,且倾斜角为π/6的直线交双曲线于AB两点,求△F1AB面积
答
c²=a²+b² =9 直线AB:y = -x/√3 + √3带入双曲线:5x² +6x -27 = 0(x1-x2)² =(x1+x2)² -4x1x2=576/25(y1-y2)²=(x1-x2)²/3=192/25AB² = 768/25AB=16√3/5AB边是的高=3...