lyhxy1997
幼苗
共回答了16个问题采纳率:87.5% 举报
答:
y=x+m代入椭圆x²/4+y²=1有:
x²+4(x+m)²-4=0
5x²+8mx+4m²-4=0
根据韦达定理:
x1+x2=-8m/5
x1x2=(4m²-4)/5
原点(0,0)到直线y=x+m的距离:
d=|0-0+m|/√(1²+1²)=|m|/√2(点到直线的距离公式)
AB²=(x1-x2)²+(y1-y2)²=2(x1-x2)²=2(x1+x2)²-8x1x2
所以:
AB²=2*(-8m/5)²-8*(4m²-4)/5
=128m²/25-(32m²-32)/5
=(128m²-160m²+160)/25
=(160-32m²)/25
AB=(4/5)*√(10-2m²)
面积S=AB*d/2
=(4/5)*√(10-2m²) *(1/2)*|m|/√2
=(√2/5)*√ [(10-2m²)m² ]
=(2/5)* √ [(5-m²)m²]
当5-m²=m²即m²=5/2时面积S取得最大值1
1年前
9