If 3 x^2-11 x y+10 y^2-7 x+13 y+k=0 denotes a pair of straight lines, then the point of intersection of the lines is

Step-by-step solution

The pair of straight lines is 3 x^2-11 x y+10 y^2-7 x+13 y+k=0 then on compairing with a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 array l a=3, h=- 11 2 , b=10 g=- 7 2 , f= 13 2 , c=k array . Then, the point of intersection of the lines is h f-b g a b-h^2 , g h-a f a b-h^2 ]= [ -143 4 + 70 2 30- 121 4 , 77 4 - 39 2 30- 121 4 ]= [ -3 120-121 , 77-78 120-121 ]= ( -3 -1 , -1 -1 )=(3,1)