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A circle centre (1,2) touches y-axis. Ra...

A circle centre (1,2) touches y-axis. Radius of the circle is

A

2

B

3

C

1

D

4

Text Solution

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The correct Answer is:
To find the radius of the circle with center at (1, 2) that touches the y-axis, we can follow these steps: ### Step 1: Understand the position of the center The center of the circle is given as (1, 2). This means that the circle is located 1 unit away from the y-axis (which is the line x = 0) and 2 units above the x-axis (which is the line y = 0). **Hint:** The center's x-coordinate indicates how far the circle is from the y-axis. ### Step 2: Determine the distance from the center to the y-axis Since the circle touches the y-axis, the radius of the circle is equal to the horizontal distance from the center of the circle to the y-axis. The y-axis is represented by the line x = 0. **Hint:** The radius is the same as the distance from the center to the nearest point on the y-axis. ### Step 3: Calculate the radius The distance from the center (1, 2) to the y-axis (x = 0) is simply the x-coordinate of the center, which is 1. Therefore, the radius of the circle is 1 unit. **Hint:** The radius can be found by taking the absolute value of the x-coordinate of the center since it represents the distance to the y-axis. ### Conclusion The radius of the circle is 1. **Final Answer:** The radius of the circle is 1.
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