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Question

The circles x2+y2+4x-4y+4=0 touches


A

X-axis

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B

Y-axis

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C

X-axis and Y-axis

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D

None of these

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Solution

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 x2+y2+4x-4y+4=0,

The centre is(−2,2)and the radius is2.

The distance of the centre (−2,2) from the coordinate axes is2 because the distance will be equal to the radius.

Hence, the circle touches both coordinate axes.

Therefore, the correct answer is option (C).


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