问题描述: 直线x-y+1=0被椭圆x²÷16+y²÷4=1截得的弦长为多少, 1个回答 分类:数学 2014-11-06 问题解答: 我来补答 x-y+1=0y=x+1代入x²÷16+y²÷4=1x²÷16+(x+1)²÷4=1x²+4(x+1)²=165x²+8x-12=0根据韦达定理:x1+x2=-8/5,x1x2=-2/5(x2-x1)² = (x2+x1)² -4x1x2 = (8/5)²+412/5 = 304/25(y2-y1)² = (x2+1-x1-1)² = (x2-x1)² = 304/25截得的弦长 = √{(x2-x1)²+(y2-y1)²} = √{608/5) = 4√38/5 展开全文阅读