If the line x + 2by + 7 = 0 is a diameter of | vedclass

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(D) The equation of the circle is $x^2 + y^2 - 6x + 2y = 0$.Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $2g = -6 \Righ

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$5$

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(D) The equation of the circle is $x^2 + y^2 - 6x + 2y = 0$.Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $2g = -6 \Rightarrow g = -3$ and $2f = 2 \Rightarrow f = 1$.The center of the circle is $(-g, -f) = (3, -1)$.Since the line $x + 2by + 7 = 0$ is a diameter,the center of the circle must lie on this line.Substituting $(3, -1)$ into the line equation: $3 + 2b(-1) + 7 = 0$.$10 - 2b = 0$.$2b = 10 \Rightarrow b = 5$.

If the line $x + 2by + 7 = 0$ is a diameter of the circle $x^2 + y^2 - 6x + 2y = 0$,then $b = $

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