The line \(x+y = 1 \) in \(xy\) plane bisects TWO DISTINCT chords of a standard parabola (which is symmetric about the
x-axis and whose vertex is the origin having latus rectum length = 4a) .
if it is given that the intersection point of the two chords is (a,2a) .
find the sum of all integral values of the possible lengths of latus rectum of the parabola .
Details And Assumptions
Latus rectum is the focal chord of the parabola which is perpendicular to its axis .
if your answers are 5,6 and 7 then provide the answer as 5+6+7 = 18
if you think no such parabola is possible give the answer as 0 .