If the slope of one of the lines represented by a x 2 + 2 h x y + b y 2 = 0 be the square of the other, then a + b h + 8 h 2 a b is

Step-by-step solution

a x 2 + 2 h x y + b y 2 = 0 Let the slopes of the lines represented be m ,   m 2 ∴     m + m 2 = - 2 h b   a n d   m m 2 = a b ⇒     m 3 = a b Now, m 1 + m = - 2 h b On cubing both sides, we get m 3 1 + m 3 + 3 m 1 + m = - 8 h 3 b 3 ⇒ a b 1 + a b + 3 - 2 h b = - 8 h 3 b 3 ⇒ b + a b - 6 h b = - 8 h 3 a b 2 ⇒ b + a + 8 h 3 a b = 6 h ⇒ b + a h + 8 h 2 a b = 6