Which of the following equations correctly represents a circle centered at the
origin with a radius of 7?

(C)

Step-by-step explanation:

Alright, lets get started.

The standard equation of a circle is given by :

Where (h,k) is the center of circle and r is the radius of circle.

As per given question, center should be origin, it means the center should be

As per given question, radius should be 7, it means

Plugging the value of (h,k) and r in standard equation of circle,

...... Answer (C)

Hope it will help :)