Question

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

• A. $X-$axis
• B. $Y-$axis
• C. $X-$axis and $Y-$axis
• D. None of these

Answer 1

The correct option is C

$X-$axis and $Y-$axis

Finding the distance between the center and the coordinate axes:

Given,

The equation of the circle is ${\mathrm{x}}^2+{\mathrm{y}}^2+4\mathrm{x}-4\mathrm{y}+4=0$,

The centre is$(-2,2)$and the radius is$2.$

The distance of the centre $(-2,2)$ from the coordinate axes is$2$ because the distance will be equal to the radius.

Hence, the circle touches both coordinate axes.

Therefore, the correct answer is option (C).