Geometry

Question Analysis

The main focus is to analyze the equation of the circle in standard form to identify the center coordinates and the radius, and then determine which statement is incorrect by comparing with the correct values.

Key Concept Explanation

The standard form of a circle's equation is , where  represents the center of the circle and  is the radius.

Step - by - Step Solution

1. Identify the center and radius from the equation:

Given the equation , we can rewrite  as .

Comparing with the standard form , we have , , and .

Taking the square root of both sides of , we get  (since the radius is non-negative).

2. Analyze each statement:

A."The x-coordinate of the center is ": Since , this statement is true.

B."The y-coordinate of the center is ": Since

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