Geometry

Question Analysis

The main focus is to determine the center of the circle from the given equation . The equation is in a form related to the standard form of a circle, and we need to understand how to identify the center based on the equation's structure.

Key Concept Explanation

The standard form of a circle's equation is , where  is the center of the circle and  is the radius. When the equation of a circle is in the form  (in this case ), it represents a circle centered at the origin  because it can be rewritten as  (by moving  to the right side to get ).

Step-by-Step Solution

1. Given the equation .

2. Rewrite the equation in a more recognizable form:

Add  to both sides to get .

The standard form of a circle centered at  is

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