The circle x^2+y^2+4x-4y+4=0 touches... | vedclass

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(C) Given circle equation is $x^2+y^2+4x-4y+4=0$.Comparing this with the general form $x^2+y^2+2gx+2fy+c=0$,we get $g=2$,$f=-2$,and $c=4$.The center o

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$X$-axis and $Y$-axis

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(C) Given circle equation is $x^2+y^2+4x-4y+4=0$.Comparing this with the general form $x^2+y^2+2gx+2fy+c=0$,we get $g=2$,$f=-2$,and $c=4$.The center of the circle is $(-g, -f) = (-2, 2)$.The radius of the circle is $r = \sqrt{g^2+f^2-c} = \sqrt{2^2+(-2)^2-4} = \sqrt{4+4-4} = \sqrt{4} = 2$.Since the absolute value of the $x$-coordinate of the center is $|-2| = 2$ (which equals the radius) and the absolute value of the $y$-coordinate of the center is $|2| = 2$ (which also equals the radius),the circle touches both the $X$-axis and the $Y$-axis.

The circle $x^2+y^2+4x-4y+4=0$ touches...

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