The circle x^2 + y^2 + 6y = 0 touches: | vedclass

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

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$x$-axis at the origin

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(B) The given equation of the circle is $x^2 + y^2 + 6y = 0$.Comparing this with the general equation $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = 0$,$f = 3$,and $c = 0$.The center of the circle is $(-g, -f) = (0, -3)$.The radius of the circle is $R = \sqrt{g^2 + f^2 - c} = \sqrt{0^2 + 3^2 - 0} = 3$.Since the center is $(0, -3)$ and the radius is $3$,the distance from the center to the $x$-axis is $|-3| = 3$,which is equal to the radius.Therefore,the circle touches the $x$-axis at the point $(0, 0)$,which is the origin.

The circle $x^2 + y^2 + 6y = 0$ touches:

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