In the parabola y2=4ax the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord is
The length of the latus rectum of the parabola y2=4ax is 4a. Given that the length of the latus rectum is 6 units, we have 4a=6. Therefore, a=‌
3
2
. The equation of the parabola becomes y2=6x. The vertex of the parabola is at the origin (0,0), and the negative end of the latus rectum is at the point (−a,2a), which is (−‌
3
2
,3) in this case. The slope of the chord passing through the vertex and the negative end of the latus rectum is ‌
3−0
−‌
3
2
−0
=−2. The equation of the chord in point-slope form is y−0=−2(x−0), which simplifies to y=−2x Therefore, the equation of the chord is 2x+y=0. The correct option is B.