If the slope of one line is twice the slope of other in the pair of straight lines a x^2+2 h x y+b y^2=0 , then 8 h^2 is equal to

Step-by-step solution

Given pair of straight lines is a x^2+2 h x y+b y^2=0 Here, m₁=2 m₂ (given) ...(i) Since, m₁+m₂= -2 h b ...(ii) and m₁ m₂= a b ...(iii) From Eqs. (i) and (ii) aligned 2 m₂+m₂ & =- 2 h b 3 m₂ & = -2 h b aligned ...(iv) From Eqs. (i) and (iii) aligned 2 m₂ m₂ & = a b 2 m₂^2 & = a b aligned (v) From Eqs. (iv) and (v) gathered 2 ( -2 h 3 b )^2= a b 2 4 h^2 9 b^2 = a b 8 h^2=9 a b gathered