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 .

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 .


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