Question

If a circle with radius 2 units touches the x-axis at (1, 0) then its center may be:

• A. $(\pm 1,2)$
• B. $(\pm 1,\pm 2)$
• C. $(1,\pm 2)$
• D. $(1,\pm \sqrt{5})$

Answer 1

The correct option is C $(1,\pm 2)$

If $x^2+y^2+2gx+2fy+c=0$ touches x−axis

then r=|f| wherer is radius of cirlce and $(-g,-f)$ is centre of circle

Given that $r=2\Rightarrow |f|=2\Rightarrow f=\pm 2$

Cirlce touches $x$axis at (1,0),

hence centre of cirlce may be (1,5) or (1,−2)