Let theLmakes and angleθfrom positive direction ofX-axis. ∴The equation of L is
x−1
cosθ
=
y−5
sinθ
=r and −r LetA(rcosθ+1,rsinθ+5)andB(−rcosθ+1,−rsinθ+5) be two points which lies in the given two lines5x−y−4=0and 3x+4y−4=0 because L bisects these lines. 5(rcosθ+1)−rsinθ−5−4=0 3(−rcosθ+1)+4(−rsinθ+5)−4=0 r(5cosθ−sinθ)=4....(i) r(−3cosθ−4sinθ)=−19....(ii) From Eqs. (i) and (ii) −95cosθ+19sinθ=−12cosθ−16sinθ ⇒35sinθ=83cosθ ∴tanθ=
