If h^2=a b , then the slopes of lines represented by a x^2-2 h x y+b y^2=0 would be in the ratio

Step-by-step solution

Given, h^2=a b and a x^2+2 h x y+b y^2=0 Divide by x^2 , we obtain b m^2+2 h m+a=0 [ y=m x is equation of line through origin, i.e. . y x =m ] aligned m & = -2 h 4 h^2-4 a b 2 b & = -2 h 4 (h^2-a b ) 2 b ( h^2=a b and h^2-a b=0 ) & = -2 h 2 b m₁ & = h b and m₂= h b aligned Therefore, slopes of both lines are equal m₁: m₂=1: 1