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Pair of lines through (1, 1) and making...

Pair of lines through `(1, 1)` and making equal angle with `3x - 4y=1` and `12x +9y=1` intersect x-axis at `P_1` and `P_2` , then `P_1,P_2` may be

A

`((8)/(7),0)` and `((9)/(7),0)`

B

`((6)/(7),0)` and `(8,0)`

C

`((8)/(7),0)` and `((1)/(8),0)`

D

`(8,0)` and `((1)/(8),0)`

Text Solution

Verified by Experts

The correct Answer is:
B
Lines making equal angle with given two lines are always parallel to angle bisectors
Equation of angle bisectors `(3x-4y-1)/(5) =(12x+9y-1)/(15)`
So bisectors have slope `7,-(1)/(7)`
Equation of required lines `y - 1 = 7(x-1)` and `y -1 =-(1)/(7) (x-1)` which intersect x-axis at `((6)/(7),0)` and (8,0).
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