# Conics Strike Again!

Geometry Level 5

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 .