Correct option is C. 2x + y = 0
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 = \(\sqrt{a^2+b^2-c}\)
For x2 + y2 - 2x + 4y = 0
⇒ 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