y=kx+m与x^2/4+y^2/5=1交于A,B且Koa×Kob=-3/4

y=kx+m与x^2/4+y^2/5=1交于A,B且Koa×Kob=-3/4

把y=kx+m①代入5x^2+4y^2=20得
5x^2+4(k^2x^2+2kmx+m^2)=20,
整理得(5+4k^2)x^2+8kmx+4m^2-20=0,
△/16=4k^2m^2-(5+4k^2)(m^2-5)
=20k^2+25-5m^2,
设A(x1,y1),B(x2,y2),则
|AB|=√[△(k^2+1)]/(5+4k^2),
x1+x2=-8km/(5+4k^2),x1x2=(4m^2-20)/(5+4k^2),
由①，y1y2=(kx1+m)(kx2+m)
=k^2x1x2+km(x1+x2)+m^2
=[k^2(4m^2-20)-8k^2m^2+m^2(5+4k^2)]/(5+4k^2)
=(5m^2-20k^2)/(5+4k^2),
∴kOA*kOB=y1y2/(x1x2)=(5m^2-20k^2)/(4m^2-20)=-3/4,
∴5m^2-20k^2=-3m^2+15,
∴m^2=(20k^2+15)/8.②
O到直线①的距离h=|m|/√(k^2+1),
∴S△OAB=(1/2)|AB|h=2|m|√(20k^2+25-5m^2)/（5+4k^2）
=2√[(20k^2+15)(60k^2+125)]/[8(5+4k^2)]（由②)
=(5/4)√[(4k^2+3)(12k^2+25)]./(5+4k^2).

2.看不清。