If the line passing through `P(1,2)` making an angle `45^(@)` with the x-axis in the positive direction meets the pair of lines `x^(2) +4xy +y^(2) = 0` at A and B then `PA. PB =`A. `13//3`B. `13//6`C. `11//6`D. `11//3`

If the line passing through `P(1,2)` making an angle `45^(@)` with the

1.	If the line passing through `P(1,2)` making an angle `45^(@)` with the x-axis in the positive direction meets the pair of lines `x^(2) +4xy +y^(2) = 0` at A and B then `PA. PB =`A. `13//3`B. `13//6`C. `11//6`D. `11//3`
Answer» Correct Answer - A Any point at distance r from the point `P(1,2)` on the line making an angle `45^(@)` with the x-axis is `(1+(r )/(sqrt(2)),2+(r )/(sqrt(2)))` Solving this point with the given pair of lines `x^(2)+4xy +y^(2) =0`, we get `3r^(2) +9sqrt(2)r +13 =0` Product of roots `r_(1)r_(2) = 13//3`

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