Find the coordinates of the points where a circle of radius , centered on the point with coordinates (1, 1) cut the axes.

Let the coordinates of the required point is (x, y).

Since the point is on the circle,

Its distance from the centre(1,1) = Radius =

⇒ = √2

⇒ (x – 1)² + (y – 1)² = 2

If the point is on X axis,

y = 0

⇒ (x – 1)² + (0 – 1)² = 2

⇒ (x – 1)² + 1 = 2

⇒ (x – 1)² = 1

⇒ x – 1 = 1 or x – 1 = – 1

⇒ x = 2 or x = 0

Hence, coordinates of the points where a circle of radius √2, centred on the point with coordinates (1, 1) cut the axis are (2,0)and (0,0)

If the point is on Y axis,

x = 0

⇒ (0 – 1)² + (y – 1)² = 2

⇒ (– 1)² + (y – 1)² = 2

⇒ (y – 1)² = 1

⇒ y – 1 = 1 or y – 1 = – 1

⇒ y = 2 or y = 0

Hence, coordinates of the points where a circle of radius √2, centred on the point with coordinates (1, 1) cut the axis are (0,2)and (0,0)

Hence, the coordinates of the points where a circle of radius _√2, centred on the point with coordinates (1, 1) cut the axes are (0,0),(2,0) and (0,2).