JEE Main 2016 (7)

Geometry Level 4

Find the sum of slopes of all possible lines passing through origin \(O\) and intersecting the lines \(x+y=1,x+2y=1\) at \(A,B\) respectively such that \(3(OA)(OB)=1\).

Note: \(OA\) represents distance between origin and point \(A\).