The equation of a circle in standard form is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:
- \( (h, k) \) is the center of the circle.
- \( r \) is the radius.

In your case, the center \( C(0, 0) \) has coordinates \( h = 0 \) and \( k = 0 \), and the radius \( r = 4 \).

Substitute these values into the standard form equation:

\[
(x - 0)^2 + (y - 0)^2 = 4^2
\]

Simplifying this:

\[
x^2 + y^2 = 16
\]

This is the equation of the circle in standard form.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How do you find the equation of a circle if the center is not at the origin?
2. What is the general form of the equation of a circle, and how does it relate to the standard form?
3. How would the equation change if the radius were doubled?
4. How can you derive the equation of a circle given three points on the circumference?
5. What are the differences between the equations of a circle and an ellipse?

**Tip:** Always double-check the sign and values for the center coordinates in the standard form equation!

Discover how to write the equation of a circle in standard form, given the center at (0,0) and radius 4. Learn key geometry concepts, including the standard circle equation and its application to coordinate geometry. Perfect for high school students in Grades 9-12.

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