数学椭圆求抛物线y^2=12x截直线y=2x+1所得的弦长.
求抛物线y^2=12x截直线y=2x+1所得的弦长.
以题中直线代入抛物线并整理易得x^2-2x+1/4=0,故(x1-x2)^2=(x1+x2)^2-4x1x2=2^2-4*1/4=3; (y1-y2)^2=4(x1-x2)^2=12.故弦长L=根号[(x1-x2)^2+(y1-y2)^2]=根[3+12]=根15。