⑴将椭圆方程化为
2x2/5m2+2y2/3m2=1,则F(m,0)
设A(x1,y1),B(x2,y2)则M(x1+x2/2,y1+y2/2)
LAB:y=k(x-m)代入椭圆方程根据韦达定理可得
x1+x2=10k2m/5k2+3,
∴y1+y2=-6km/5k2+3
∴M(5k2m/5k2+3,-3km/5k2+3)
∴Kom=-3/5k,设LMN:y=-3x/5k代入椭圆方程求得Xn=|5km|/√10k2+6∵向量OA+向量OB=向量ON,∴x1+x2=xn代入化简得K=±1
⑵本小问只需将A,B点坐标代入化简就可求得K的取值范围