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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Solution

(c) 2x + y = 0

Let the diameter of the circle be y = mx.
Since the diameter of the circle passes through its centre, (1, −2) satisfies the equation of the diameter.
∴ $m = - 2$

Substituting the value of m in the equation of diameter:
$y = - 2 x$
$\Rightarrow 2 x + y = 0$

Hence, the required equation of the diameter is $2 x + y = 0$ .

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