Question

The equation of the circle in the first quadrant touching each coordinate axes at a distance of one unit from the origin is
(a) x² + y² – 2x – 2y + 1 = 0
(b) x² + y² – 2x – 2y – 1 = 0
(c) x² + y² – 2x – 2y = 0
(d) x² + y² – 2x + 2y – 1 = 0

Answer 1

Since the circle touches both the axis and has radius 1.
i.e. distance of center from x and y axis is 1.
i.e. equation of circle is
(x − 1)² + (y − 1)² = 1²
i.e. x² − 2x + 1 + y² − 2y + 1 = 1
i.e. x² + y² − 2x − 2y + 1 = 0

Hence, the correct answer is option A.