The radius of a circle touching x-axis and having centre (2, 4) is

Options

A. 2
B. 4
C. 6
D. none

Answer

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

### Step-by-Step Solution:

1. **Identify the Center of the Circle**:
The center of the circle is given as \( C(2, 4) \).

2. **Understand the Position of the Circle**:
Since the circle touches the x-axis, the distance from the center of the circle to the x-axis is equal to the radius of the circle.

3. **Calculate the Distance from the Center to the x-axis**:
The y-coordinate of the center gives us the vertical distance to the x-axis. Here, the y-coordinate is 4.

4. **Determine the Radius**:
Therefore, the radius \( r \) of the circle is equal to the y-coordinate of the center, which is 4 units.

5. **Conclusion**:
The radius of the circle is \( 4 \) units.

### Final Answer:
The radius of the circle is \( 4 \) units.

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