Question

已知通过点(0,3)的直线被抛物线x^2=y所截得的弦长等于4√5,求该直线方程

Answer 1

直线不与y轴平行,可设方程y=kx+3联立直线与抛物线方程得：x^2-kx-3=0弦长√[(x1-x2)^2+(y1-y2)^2]=√[(k^2+1)(x1-x2)^2] =√{(k^2+1)[(x1+x2)^2-4x1x2]} =√(k^2+1)(k^2+12) =4√5k^2=4k=±2直线方程是y=2x+3或y=-2x+3