Consider the circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$ Does this touch the coordinate axes?

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Solution

Putting y=0 in equation of circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$
We get $x^{2} + 4 x + 4 = 0 \Rightarrow (x + 2)^{2} = 0 \Rightarrow$ circle touch the X axis at (-2,0)
Putting x=0 in equation of circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$
We get $y^{2} - 4 y + 4 = 0 \Rightarrow (y - 2)^{2} = 0 \Rightarrow$ circle touch the Y axis at (0,2)
Then equation of circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$ touches he coordinate axes.

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