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Equation of the diameter of the circle x2 + y2 – 2x + 4y = 0 which passes through the origin is

A. x + 2y = 0

B. x - 2y = 0

C. 2x + y = 0

D. 2x - y = 0

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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

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