If the equation 3 x²+10 x y+3 y²+16 y+k=0 represents a pair of lines, then the value of k is

Step-by-step solution

(A) Comparing the given equation with a x²+2 h x y+b y²+2 g x+2 f y+c=0 , we get, a=3, h=5, b=3, g=0, f=8, c=k . Now, given equation represents a pair of lines. a b c+2 f g h-a f²-b g²-c h²=0 (3) (3) ( k )+2(8)(0)(5)-3(8)²-3(0)²- k (5)²=0 9 k +0-192-0-25 k =0 16 k =-192 k =-12