If the pair of straight lines x y-x-y+1=0 and the line a x+2 y-3 a=0 are concurrent, then a is equal to

Step-by-step solution

We have, array r x y-x-y+1=0 a x+2 y-3 a=0 array and Eqs. (i) with, On comparing Eqs. (i) with, a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 , we get a=0, b=0, h= 1 2 , g=- 1 2 , f=- 1 2 , c=1 The point of concurrent is ( h f-b g a b-h^2 g h-a f a b-h^2 ) = ( 1 2 (- 1 2 )-0 0- ( 1 2 )^2, (- 1 2 ) ( 1 2 )-0 0- ( 1 2 )^2 )=(1,1) This point lies on equation (ii), then array rlrl & a+2-3 a & =0 2 a=2 & & a & =1 array