已知斜率为k的直线l与椭圆C:x2/4+y2/3=1交于AB两点线段AB的中点为M...答:设l:y=kx+n,代入x^2/4+y^2/3=1,得 3x^2+4(k^2x^2+2knx+n^2)=12,(3+4k^2)x^2+8knx+4n^2-12=0,△/4=16k^2n^2-(3+4k^2)(4n^2-12)=36+48k^2-12n^2>0,n^2<3+4k^2,① 设A(x1,y1),B(x2,y2),则x1+x2=-8kn/(3+4k^2),线段AB的中点为M(1,m),...
...设斜率为k的直线l,交椭圆C与A,B两点,AB的中点为M,证答:证明: 设A(x1,y1),B(x2,y2),M(x,y).∵ (x1/a)^2+(y1/b)^2=1...①,(x2/a)^2+(y2/b)^2=1...②,①-②得(x1+x2)(x1-x2)/a^2+(y1+y2)(y1-y2)/b^2=0,∵ x1+x2=2x, y1+y2=2y,k=(y1-y2)/(x1-x2),∴ (x/a^2)+ky/(b^2)=0.∴ 动点M在...