The joint equation of lines passing through the origin and trisecting the first quadrant is ________

Step-by-step solution

As given, both line passes through 0 , 0 a n d θ 1 = π 6 , θ 2 = π 3 ∴ Equation of first line is. y - 0 = tan ⁡ π 6 x - 0 ⇒ y = 1 3 x ⇒ x - 3 y = 0 ...... (i) Equation of second line is y - 0 = tan ⁡ π 3 ( x - 0 ) ⇒ y = 3 x ⇒ 3 x - y = 0 ...... (ii) Hence, joint equation of these line is x - 3 y 3 x - y = 0 ⇒ 3 x 2 - x y - 3 x y + 3 y 2 = 0 ⇒ 3 x 2 + 3 y 2 - 4 x y = 0