设m(x1,y1),n(x2,y2)
∵OM ⊥ON
∴x1·x2+y1y2=0
将mx+ny=1代入x²+2y²=1
x1x2=(2-n²)/(n²+2m²)【根据x1x2=c/a】
y1y2=(1-m²)/(n²+2m²)
∴x1·x2+y1y2=(3-n²-m²)/(n²+2m²)=0
∴3-n²-m²=0
即m²+n²=3
设m(x1,y1),n(x2,y2)
∵OM ⊥ON
∴x1·x2+y1y2=0
将mx+ny=1代入x²+2y²=1
x1x2=(2-n²)/(n²+2m²)【根据x1x2=c/a】
y1y2=(1-m²)/(n²+2m²)
∴x1·x2+y1y2=(3-n²-m²)/(n²+2m²)=0
∴3-n²-m²=0
即m²+n²=3