Find the equation of the diameter of the circ | vedclass

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(C) The given circle is $x^2 + y^2 - 4x + 2y - 11 = 0$. Comparing with $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -2$ and $f = 1$. The center of the

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$2x + y - 3 = 0$

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(C) The given circle is $x^2 + y^2 - 4x + 2y - 11 = 0$. Comparing with $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -2$ and $f = 1$. The center of the circle is $(-g, -f) = (2, -1)$. The system of parallel chords is given by $x - 2y + c = 0$. The diameter corresponding to this system of parallel chords is the line perpendicular to the chords and passing through the center of the circle. The slope of the chords is $m = 1/2$. The slope of the diameter is $m' = -1/m = -2$. The equation of the diameter passing through $(2, -1)$ with slope $-2$ is: $y - (-1) = -2(x - 2)$ $y + 1 = -2x + 4$ $2x + y - 3 = 0$.

Find the equation of the diameter of the circle $x^2 + y^2 - 4x + 2y - 11 = 0$ which corresponds to the system of parallel chords $x - 2y + c = 0$.

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