Question

The circle ${\mathrm{x}}^2+{\mathrm{y}}^2+4\mathrm{x}-4\mathrm{y}+4=0$ touches

• A. $x-axis$
• B. $y-axis$
• C. $x-axisandy-axis$
• D. None of These

Answer 1

The correct option is C

$x-axisandy-axis$

Explanation for the correct option:

Finding the coordinate axes to which the circle touches:

${\mathrm{x}}^2+{\mathrm{y}}^2+4\mathrm{x}-4\mathrm{y}+4=0$

Comapring with ${\mathrm{x}}^2+{\mathrm{y}}^2+2g\mathrm{x}+2f\mathrm{y}+c=0,wherecentre=(-g,-f),r=\sqrt{g^2+f^2-c}$

The centre is $(-2,2)$ and the radius is $\sqrt{2^2+2^2-4}=2$

The distance of the centre $(-2,2)$ from the coordinate axes is equal to $2$

Hence, the circle touches both coordinate axes, and the points of contact are given by $(-2,0)$and $(0,2).$

Therefore, the correct answer is option (C).