If m is the slope of one of the lines represented by a x²+2 h x y+b²=0 , then (h+b m)² is equal to

Step-by-step solution

Given that, a x²+2 h x y+b y²=0 ...(i) Which is homogeneous equation representing pair of straight line each of which passing through the origin. Given one slope of line = m . Let another slope of line =m₁ Then, the lines are y=m x and y=m₁ x Now, ( mx - y ) ( m ₁ x - y ) mm ₁ x ²- m ₁ xy - mxy + y ² mm ₁ x ²- ( m + m ₁ ) y x + y ² ...(ii) On comparing Eqs. (i) and (ii), aligned m + m ₁ &=- 2 ~h ~b ...(iii) ~mm ₁ &= a b ...(iv) aligned From Eqs. (iii) and (iv), m ₁= (- 2 ~h ~b - m ) array lc & m ( -2 ~h ~b - m )= a