Question

The lines joining the origin to the points of intersection of 2x^2+3xy-4x+1=0 and 3x+y=1 is given by?

Answer 1

pair of st lines in L ≡ 2x² + 3xy - 4x + 1 = 0

dL/dx = 4x + 3y -4 = 0 ⇒ L₁
dL/dy = 3x = 0 ⇒ x = 0  ⇒ L₂

L ≡ 3x + y = 1         

intersection of L₁ and L gives A ( -1/5 , 8/5 )
and intersection of L₂ and L gives B (0, 1)

now l₁ passing origin and A  is given by  y + 8x = 0
and l₂ passing through origin and B is given by x = 0

so pair of straight lines is (y+8x)(x) = 0

hope my ans is correct.