Question

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

• A. x-axis only
• B. y- axis only
• C. Both x and y- axis
• D. Does not touch any axis

Answer 1

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.