The eqn of a straight lin passing through (1,2) and having intercept of length 3 between the straight lines 3x + 4y=12 and 3x+4y =24 is,a) 7x+34y-35=0b)24x+7y-38=0c) 24x-7y-10=0d)7x-24y+41=0

I think the intercept distance sud be more than 3 otherwise if it is 3 the line wud be parallel to the y axis.

Isnt there a shorter method? The method you have suggested is quite lenghty and consumes a lot of time.