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

The circle $x^2+y^2+4 x-4 y+4=0$ touches...
  1. $X$-axis only
  2. $Y$-axis only
  3. $X$-axis and $Y$-axis
  4. $x=y$

Solution

Given circle (c), $x^2+y^2+4 x-4 y+4=0$ On comparing with its general form $x^2+y^2+2 g x+2 f y+c=0$ whose center $=(-g,-f)$ and radius $=\sqrt{g^2+f^2-c}$ $\Rightarrow \quad g=2, f=-2, c=4$ $\therefore$ Center $=(-2,2)$ and radius $=\sqrt{4+4-4}=2$ With the help of diagram, we can see that it touches $X$-axis and $Y$-axis.

Asked in: AP EAMCET 2021 (23 Aug Shift 2)

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