F,E为椭圆左右焦点,过F斜率为1的直线与椭圆交于点AB且AE,AB,BE成等差数列求椭圆离心率?p(0,-1)满足pA=pB求椭圆方程?
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![F,E为椭圆左右焦点,过F斜率为1的直线与椭圆交于点AB且AE,AB,BE成等差数列求椭圆离心率?p(0,-1)满足pA=pB求椭圆方程?](/uploads/image/z/3704033-65-3.jpg?t=F%2CE%E4%B8%BA%E6%A4%AD%E5%9C%86%E5%B7%A6%E5%8F%B3%E7%84%A6%E7%82%B9%2C%E8%BF%87F%E6%96%9C%E7%8E%87%E4%B8%BA1%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%A4%AD%E5%9C%86%E4%BA%A4%E4%BA%8E%E7%82%B9AB%E4%B8%94AE%2CAB%2CBE%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E6%B1%82%E6%A4%AD%E5%9C%86%E7%A6%BB%E5%BF%83%E7%8E%87%3Fp%EF%BC%880%2C-1%EF%BC%89%E6%BB%A1%E8%B6%B3pA%3DpB%E6%B1%82%E6%A4%AD%E5%9C%86%E6%96%B9%E7%A8%8B%3F)
F,E为椭圆左右焦点,过F斜率为1的直线与椭圆交于点AB且AE,AB,BE成等差数列求椭圆离心率?p(0,-1)满足pA=pB求椭圆方程?
F,E为椭圆左右焦点,过F斜率为1的直线与椭圆交于点AB且AE,AB,BE成等差数列求椭圆离心率?p(0,-1)满足pA=pB求椭圆方程?
F,E为椭圆左右焦点,过F斜率为1的直线与椭圆交于点AB且AE,AB,BE成等差数列求椭圆离心率?p(0,-1)满足pA=pB求椭圆方程?
我们设A(x1,y1)B(x2,y2),AB中点M(xo,yo),由题有2AB=AE+BE=(2a-AF)+(2a-BF)=4a-AB,于是AB=4a/3,可设直线AB方程为:y=x+c,联立x^2/a^2+y^2/b^2=1消去y得:(a^2+b^2)x^2+2a^2cx+a^2(c^2-b^2)=o,于是x1+x2=-2a^2c/(a^2+b^2)=2xo.(1);x1x2=a^2(c^2-b^2)/(a^2+b^2),又AB=(1+k^2)^0.5[(x1+x2)^0.5-4x1x2)]^0.5,其中k=1,a^2-b^2=c^2.代入化简整理得AB=4ab^2/(a^2+b^2)=4a/3,得到a^2=2b^2=2(a^2-c^2),即a^2=2c^2,所以离心率e=1/(2^0.5).用点差法.x1^2/a^2+y1^2/b^2=1;x2^2/a^2+y2^2/b^2=1,相减得KAB=(y1-y2)/(x1-x2)=-(b^2/a^2)(x1+x2)/(y1+y2)=-(1/2)(xo/yo)=1,由题易知PM垂直AB,则KPM=(yo+1)/xo=-1,联立两式得yo=1,xo=-2,代入(1)式并注意到a^2=2b^2=2c^2,可得c=3,a^2=18,b^2=9进而知所求椭圆方程为x^2/18+y^2/9=1.仅供参考哈.
我有一处笔误弦长公式中(x1+x2)^0.5应写成(x1+x2)^2