Question

The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is :

• A. $x^2+y^2-2x-2y+1=0$
• B. $x^2+y^2-2x-2y-1=0$
• C. $x^2+y^2-2x-2y=0$
• D. $x^2+y^2-2x+2y-1=0$

Answer 1

The correct option is A $x^2+y^2-2x-2y+1=0$

The circle touches the $x$ and $y$ axes at $(1,0)$ and $(0,1)$ respectively.

Since tangents are perpendicular to radii at the points of contact, its center must be at the point $(1,1)$. Clearly, its radius is one unit.

So the equation of the circle is

$(x-1{)}^2+(y-1{)}^2=1\Rightarrow x^2+y^2-2x-2y+1=0$

So option A is the right answer.