Question

If the lines represented by the equation 6x² + 41xy – 7y² = 0 make angles α and β with x – axis, then tan α tan β = 

(a) -6/7

(b) -6/7

(c) -7/6

(d) 7/6

Answer 1

(a) -6/7

6x² + 41xy – 7y² = 0 ⇒ 6x² – xy + 42xy – 7y² = 0 ⇒ x (6x – y) + 7y (6x – y) = 0

(x + 7y) (6x – y) = 0 ⇒ x + 7y = 0, 6x – y = 0