Question

Find the equation of circle which lies in the first quadrant and touching coordinate axes at a distance of 2 units from origin

Answer 1

Answer:

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

⇒x

2

+y

2

−2x−2y+1=0