Geometry

Question Analysis

This question focuses on circles. The main goal is to find the circumference of the given circle, which requires determining the radius from the positions of the center and a point on the circle in the coordinate grid and then applying the circumference formula.

 

Key Concept Explanation

The formula for the circumference  of a circle is , where  is the radius of the circle. The radius is the distance from the center of the circle to any point on its circumference.

 

Step - by - Step Solution

1. Determine the radius:

The center of the circle is at  and a point on the circle is .

Since the  - coordinates of the center and the point on the circle are the same, we can find the radius using the distance formula for points with the same  - value. The distance between two points  and  is . Here,

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