Geometry

Question Analysis

The main focus is to convert the given equation of the circle from its current form to the standard form .

 

Key Concept Explanation

The general form of a circle's equation might not always be in the typical format but can be rearranged to that form. Completing the square for the terms (in this case) means taking the coefficient of the term, dividing it by 2, squaring the result, and adding it to both sides of the equation. The standard form represents a circle with center and radius .

 

Step-by-Step Solution

1. Given the equation .

First, move the term to the left side to get .

2. Complete the square for the terms:

The coefficient of is 14. Half of 14 is 7, and .

Add 49 to both sides of the equation: .

3. Rewrite the equation:

The left side can be factored as , and the right side is .

So the standard form of the equation is .

 

Option Analysis

A.

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