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

Options

A. (a) `((8)/(7),0)` and `((9)/(7),0)`
B. (b) `((6)/(7),0)` and `(8,0)`
C. (c) `((8)/(7),0)` and `((1)/(8),0)`
D. (d) `(8,0)` and `((1)/(8),0)`

Answer

B

Explanation

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).