The circle $x^{2} + y^{2} - 8 x + 4 y + 4 = 0$ touches

x-axis only

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y- axis only

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Both x and y- axis

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Does not touch any axis

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Solution

The correct option is B
y- axis only

The given equation can be written as $(x - 4)^{2} + (y + 2)^{2} = 4^{2} .$
We know that the standard equation of the circle with centre (h, k) is $(x - h)^{2} + (y - k)^{2} = r^{2} .$
Comparing the given equation with the standard equation, we get centre $\equiv$ (4, -2), and radius = 4.
Since co-ordinates of the centre of the circle are (4, -2), therefore the given circle touches y-axis only.

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