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Let \( \mathrm{L}_{1}: \mathrm{x}+\mathrm{y}=0 \) and \( \mathrm{L}_{2}: \mathrm{x}-\mathrm{y}=0 \) are tangent to a parabola whose focus is \( \mathrm{S}(1,2) \).
\( \mathrm{P} \) If the length of latus-rectum of the parabola can be expressed as \( \frac{\mathrm{m}}{\sqrt{\mathrm{n}}} \) (where \( \mathrm{m} \) and \( n \) are coprime)

W then find the value of \( (\mathrm{m}+\mathrm{n}) \).
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