A line through P (3,4) cuts the lines x = 6 and y = 8 at L and M respectively. Q is a variable point on the line such that 1PQ=1PL+1PM then the locus of Q is

Let the line be x−3cosθ=y−4sinθ=rAny point on this line be (3+rcosθ,4+rsinθ)Substituting this in y=8, we get PL= 4sinθSubstituting this in x=6 we get PM= 3cosθ1PQ=sinθ4+cosθ3⇒12=3rsinθ+4rcosθ3(y−4)+4(x−3)∴Locus is is 4x+3y-36=0