For , R ,(x-2 y-1)+ (3 x+2 y-11)=0 and (3 x+4 y-11)+ (-x+2 y-3)=0 represent two families of lines. If the equation of the line common to both the families is a x+b y-5=0 , then 2 a+b=

Step-by-step solution

(x-2 y-1)+ (3 x+2 y-11)=0 Point of interscetion of family of lines is (3,1) . (3 x+4 y-11)+ (-x+2 y-3)=0 Point of intersection is (1,2) . Line common to 2 families is line passing throug (3,1),(1,2) . aligned & y-1 x-3 = (2-1) (1-3) -2(y-1)=x-3 & x+2 y-5=0 a=1, b-2 2 a+b=4 aligned