Given that we need to find the equation of the diameter if the circle x² + y² - 2x + 4y = 0 which passes through origin.

We know that for a circle x² + y² + 2ax + 2by + c = 0

⇒ Centre = (- a, - b)

⇒ Radius =

For x² + y² - 2x + 4y = 0

⇒ Centre(C₁) =

⇒ C₁ = (1, - 2)

We know that the diameter of the circle passes through the centre.

We need to find the equation of the diameter passing through the points (1, - 2) and (0,0)

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

⇒

⇒

⇒ y = - 2x

⇒ 2x + y = 0

∴The correct option is (c)