Question

Find the coordinates of the points where a circle of radius root2, centred on the point with coordinates (1,1) cuts the axes.​

Answer 1

Answer:

Equation of circle:(x−1)2+(y−1)2=2determine y-intercepts(y−1)2=2−(0–1)2=1y−1=±1y=1±1=2,0determine x-intercepts(x−1)2=2−(0–1)2=1x=2,0intercepts: (0,0),(0,2),(2,0),(2,2)

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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).