If a circle of radius 4 touches x-axis at (2,0) then its centre may be

Options

A. (2,2)(2,-2)
B. (2,4)(2,-4)
C. (4,2)(4,-2)
D. (4,4)(4,-4)

Answer

To find the center of a circle with a radius of 4 that touches the x-axis at the point (2, 0), we can follow these steps:

### Step 1: Understand the properties of the circle
A circle that touches the x-axis means that the distance from the center of the circle to the x-axis is equal to the radius of the circle.

### Step 2: Identify the coordinates of the touching point
The circle touches the x-axis at the point (2, 0). This means that the x-coordinate of the center of the circle is also 2, since the center must be directly above or below the touching point.

### Step 3: Determine the y-coordinate of the center
Since the radius of the circle is 4, and it touches the x-axis, the distance from the center to the x-axis must be 4 units. The center can either be above or below the x-axis:
- If the center is above the x-axis, the y-coordinate will be \(0 + 4 = 4\).
- If the center is below the x-axis, the y-coordinate will be \(0 - 4 = -4\).

### Step 4: Write the coordinates of the center
Thus, the possible coordinates for the center of the circle are:
1. \( (2, 4) \) (above the x-axis)
2. \( (2, -4) \) (below the x-axis)

### Conclusion
The center of the circle may be either \( (2, 4) \) or \( (2, -4) \).