The center of the circle, ________.
is a point on the circle
lies outside of the circle
lies inside of the circle
none of these
Hint 1: Recall the difference between the circle (the boundary curve) and the circular disk (the region inside).
Hint 2: Check if the center point satisfies the equation of the circle boundary . It does not; it lies at , which is strictly inside.
Hint 3: Select the option stating the center lies inside the circle (index 2).
Step 1 (Definition of a Circle): A circle in a plane is defined as the set of all points that are at a constant distance (the radius) from a fixed point called the center.
Step 2 (Location of the Center): By definition, the center itself does not lie on the boundary (the circle itself). Instead, it lies in the interior region enclosed by the boundary. Therefore, the center of the circle always lies inside the circle.
Step 3 (Conclusion): This matches option index 2: 'lies inside of the circle'. The correct answer is 2.
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