Give the standard equation of the circle satisfying the given condition: center at the origin, radius 4Give the standard equation of the circle satisfying the given condition: center at the origin, radius 4.

The standard equation of a circle with its center at the origin \((0, 0)\) and radius \(r\) is given by:

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

Given that the radius \(r = 4\), the equation becomes:

\[
x^2 + y^2 = 4^2
\]

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

So, the standard equation of the circle is:

\[
\boxed{x^2 + y^2 = 16}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the equation of a circle with center at \((3, -2)\) and radius 5?
2. How would you determine the radius of a circle given its equation?
3. How does the equation of a circle change if the center is not at the origin?
4. What is the general form of the equation of a circle?
5. How do you find the area of a circle given its radius?

**Tip:** Always remember that in the equation of a circle, the radius is the square root of the constant term on the right side of the equation.

Discover the standard equation of a circle with its center at the origin and radius 4. This mathematical problem explores fundamental concepts in geometry, focusing on circle equations. Suitable for students in Grades 9-12.

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