L1: x + y=0 and L2.x-y=0 are tangent to...

`L_1: x + y=0 and L_2.x-y=0` are tangent to a parabola whose focus is `S(1,2)`.If the length of latus-rectum of the parabola can be expressed as `m/sqrt(n)` (where m and n are coprime)then find the value of `(m +n)`.

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