Geometry

Question Analysis

The main focus is to convert the given circle equation from general form to standard form. We need to manipulate the equation  to match the standard - form structure . Since there are no  and  linear terms, the center is at the origin, and we just need to isolate .

 

Key Concept Explanation

The general form of a circle's equation is . When , , the circle is centered at the origin , and the standard form simplifies to , where .

 

Step - by - Step Solution

1. Given the equation .

2. Add 49 to both sides of the equation to isolate .

We get , which is in the standard form for a circle centered at the origin with radius  (since ).

 

Option Analysis

A.