橢圓X2/2+Y2=1,過(guò)左焦的直線交橢圓兩點(diǎn)A,B,線段AB的垂直平分線交X軸于點(diǎn)（m,0）求m的取值范圍

數(shù)學(xué)人氣：739 ℃時(shí)間：2020-02-04 06:12:25

優(yōu)質(zhì)解答

易得焦點(diǎn)坐標(biāo)F1(-1,0)
設(shè)AB所在直線：y=k(x+1)
聯(lián)立橢圓：(1+k²)x²+4k²x+2k²-2=0
設(shè)A(x1,y1),B(x2,y2)即x1+x2=-4k²/(1+k²),y1+y2=k(x1+k2)+2k=-4k³/(1+k²)
AB中點(diǎn)M(-2k²/(1+k²),-2k³/(1+k²))
AB的垂直平分線:y=-(x-m)/k
導(dǎo)入M點(diǎn)坐標(biāo)M(-2k²/(1+k²),-2k³/(1+k²))
進(jìn)行求值即可我很笨，怎么樣求值？-,-化簡(jiǎn)很麻煩，呵呵