For a, b, h>0 , if the slope of one of the lines represented by a^2 x^2+2 h x y+b^2 y^2=0 is twice that of the other, then the value of h a b is

Step-by-step solution

Given, lines are a^2 x^2+2 h x y+b^2 y^2=0 Let m and 2 m be the slopes of the lines. Then, m+2 m= -2 h b^2 . 3 m=- 2 h b^2 m=- 2 h 3 b^2 ...(i) and m 2 m= a^2 b^2 array ll & 2 m^2= a^2 b^2 & 2 (- 2 h 3 b^2 )^2= a^2 b^2 [from Eq. (i)] array array ll & 8 h^2 9 b^4 = a^2 b^2 h^2 a^2 b^2 = 9 8 & h a b = 3 2 2 2 2 = 3 2 4 array