Equation of the diameter of the circle $x^{2} + y^{2} - 2 x + 4 y = 0$ which passes through the origin is

$x + 2 y = 0$

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$x - 2 y = 0$

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$2 x + y = 0$

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$2 x - y = 0$

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Solution

The correct option is C
$2 x + y = 0$

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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Similar questions

The equation of the diameter of the circle $x^{2} + y^{2} + 2 x - 4 y - 11 = 0$ which bisects the chords intercepted on the line $2 x - y + 3 = 0$ is

x^{2} + y^{2} - 6 x + 2 y - 8 = 0

x^{2} + y^{2} - 2 x - 4 y + 4 = 0

x + 2 y = 4

x + 2 y = 0

x^{2} + y^{2} - 2 x + 4 y = 0

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