Let L be the line joining the origin to the point of intersection of the lines represented by 2 x^2-3 x y-2 y^2+10 x+5 y=0 . If L is perpendicular to the line k x+y+3=0 , then k is equal to

Step-by-step solution

Given that, aligned & 2 x^2-3 x y-2 y^2+10 x+5 y=0 & (2 x+y)(x-2 y+5)=0 & 2 x+y=0 and x-2 y+5=0 aligned Now, equation of line passing through origin is 2 x^2+y=0 m₁=-2 Since, this line is perpendicular to the line aligned & k x+y+3=0 m₂=-k & m₁ m₂=-1 & (-2)+(- k )=-1 k=- 1 2 aligned