Point R (h,

Let AB be the line segment such that R (h, k) divides it in the ratio 1: 2.

Let the coordinates of A and B are (0, y) and (x, 0) respectively.

We know that the coordinates of a point dividing the line segment joining the points (x₁, y₁) and (x₂, y₂) internally in the ratio m: n are .

∴

⇒

∴ h = 2x/3 and k = y/3

⇒ x = 3h/2 and y = 3k

∴ A = (0, 3k) and B = (3h/2, 0)

We know that the equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is given by

⇒ 3h(y - 3k) = -6kx

⇒ 3hy - 9hk = -6kx

⇒ 6kx + 3hy = 9hk

Dividing both the sides by 9hk, we get,