Write the equation of the circle with Center: (0,0) and radius: 7

The equation of a circle with a center at \((h, k)\) and a radius \(r\) is given by:

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

Given that the center of the circle is \((0, 0)\) and the radius is \(7\), the equation becomes:

\[
(x - 0)^2 + (y - 0)^2 = 7^2
\]

Simplifying this, we have:

\[
x^2 + y^2 = 49
\]

So, the equation of the circle is:

\[
x^2 + y^2 = 49
\]

Would you like to explore more about circles or have any other related questions?

### Relative Questions:
1. How would the equation change if the center were at \( (2, -3) \) with the same radius?
2. What is the circumference of a circle with radius 7?
3. How do you find the equation of a circle given its diameter?
4. How would you determine if a point lies on this circle?
5. What would the equation be if the radius were doubled?

### Tip:
When the center of a circle is at the origin \((0,0)\), the equation simplifies significantly to \(x^2 + y^2 = r^2\).

Learn how to write the equation of a circle with center (0,0) and radius 7 using the formula (x - h)^2 + (y - k)^2 = r^2. Understand the geometric properties and calculations involved in defining a circle based on its center and radius. Suitable for high school students and beyond.

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