椭圆焦点弦长公式的推理证明答:设焦点弦端点为A,B,A,B横坐标分别为x1,x2,A,B到与焦点对应的准线的距离分别为d1,d2,焦点弦过焦点F,则离心率e=AF/d1=BF/d2=(AF+BF)/(d1+d2)=AB/(d1+d2)=AB/[|x1-(a^2)/c|+|x2-(a^2)/c|]焦点弦长AB=e[|x1-(a^2)/c|+|x2-(a^2)/c|]若F为右焦点,则d1...
椭圆中,过焦点的弦AB被焦点分成的线段长m,n满足1/m+1/n=2a/b2的证明...答:证明:设椭圆方程x?/a?+y?/b?=1,焦点AB在x轴上,右交点B(c,0),过B点的弦CD.BC=m,BD=n.右准线x=a?/c 根据椭圆定义,设C点横坐标x,则有m/(a?/c-x)=c/a,可求出其横坐标,进而求出其纵坐标.故C点坐标可求,为C[a(a-m)/c,b/c√(-b?+2am-m?)],D[a(a-n)/c,-b/c...