設(shè)直線(xiàn)為y-2=kx
與橢圓方程X^2/2+Y^2=1聯(lián)立,得到
X^2/2+(kx+2)^2=1
(k^2+1/2)x^2+4kx+3=0
根的判別式=16k^2-12(k^2+1/2)=4k^2-6>0
k^2>2/3
x1+x2=-4k/(k^2+1/2)
x1x2=3/(k^2+1/2)
兩交點(diǎn)距離=根號(hào)下(k^2+1)乘以|x2-x1|
=根號(hào)下(k^2+1)乘以|x2-x1|
原點(diǎn)到兩交點(diǎn)所在直線(xiàn)距離
=|k*0-0+2|/根號(hào)下(k^2+1)
三角形面積
=1/2*根號(hào)下(k^2+1)乘以|x2-x1|乘以|k*0-0+2|/根號(hào)下(k^2+1)
=|x2-x1|
=根號(hào)下[(x1+x2)^2-4x1x2]
=根號(hào)下[(4k^2-6)/(k^2+1/2)^2]
=根號(hào)下[4/(k^2+1/2)-8/(k^2+1/2)^2]
=2/3
換元,令m=4/(k^2+1/2),m2/3.的條件.