If the lines x^2+2 x y-35 y^2-4 x+44 y-12=0 and 5 x+k y-8=0 are concurrent, then k equals

Step-by-step solution

Since, we know that, point of intersection of pairs of line represented by aligned & a x^2+2 h y x+b y^2+2 g x+2 f y+c=0 is & ( h f-b g a b-h^2 , g h-a f a b-h^2 ) aligned For the lines, x^2+2 x y-35 y^2-4 x+44 y-12=0a=1, h=1, b=-35, g=-2, f=22 and c=-12 aligned & ( h f-b g a b-h^2 , g h-a f a b-h^2 ) & = ( 1 22-70 -35-1 , -2-22 -35-1 )= ( -48 -36 , -24 -36 )= ( 4 3 , 2 3 ) aligned Lines are concurrent, hence array rlrl ( 4 3 , 2 3 ) must satisfy 5 x+k y-8 & =0 5 ( 4 3 )+k ( 2 3 ) & =8 20+2 k & =24 2 k=4 & k & =2 a