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If the line passing through P(1,2) makin...

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`

Text Solution

Verified by Experts

The correct Answer is:
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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