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

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answer is 11.

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Detailed Solution

$L L R = \frac{4 P_{1} P_{2}}{S T} (T i s t h e p o i n t o f i n t e r s e c t i o n o f \tan g e n t s)$

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