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Question

The circle x2+y28x+4y+4=0 touches
  1. x-axis only

  2. y- axis only

  3. Both x and y- axis
  4. Does not touch any axis


Solution

The correct option is B

y- axis only


The given equation can be written as (x4)2+(y+2)2=42.
We know that the standard equation of the circle with centre (h, k) is (xh)2+(yk)2=r2. 
Comparing the given equation with the standard equation, we get centre (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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