直线x-y+1=0被椭圆x²/16+y²/4=1截得的弦长是多少?
问题描述:
直线x-y+1=0被椭圆x²/16+y²/4=1截得的弦长是多少?
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...