The question is asking for the standard form of the equation of a circle centered at $(0, 0)$ with a radius of 8.

The general equation for a circle with center $(h, k)$ and radius $r$ is:

$(x - h)^2 + (y - k)^2 = r^2$

Since the center is $(0, 0)$ and the radius is $8$, the equation becomes:

$x^2 + y^2 = 8^2$

Simplifying this:

$x^2 + y^2 = 64$

So, the correct answer is:

$x^2 + y^2 = 64$

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:

1. How would the equation change if the circle were centered at $(2, -3)$?
2. How do you determine the radius of a circle given its equation?
3. What is the equation of a circle with radius 5 centered at the origin?
4. How can you graph the equation of a circle on the coordinate plane?
5. How does the equation change if the radius is halved?

Tip: The square of the radius appears on the right side of the equation, so always square the given radius when writing the equation of a circle.