The equation you provided, \(x^2 + y^2 = 1\), represents a circle in the Cartesian coordinate system.

### Key Details:
- **Center of the circle:** The center of the circle is at the origin \((0, 0)\).
- **Radius of the circle:** The radius \(r\) is 1, as the equation is in the standard form of a circle equation \( (x - h)^2 + (y - k)^2 = r^2 \) where \((h, k)\) is the center, and \(r\) is the radius.

This equation describes all the points \((x, y)\) that are exactly 1 unit away from the origin.

Would you like more details or have any specific questions about this equation?

Here are five related questions to expand your understanding:
1. How would the equation change if the circle had a radius of 2?
2. What would the equation be if the circle were centered at \((2, 3)\)?
3. Can you find the intersection points of this circle with the line \(y = x\)?
4. How would you write the equation of a circle that is tangent to the x-axis?
5. What is the area of the circle described by the equation \(x^2 + y^2 = 1\)?

**Tip:** For any equation of a circle, identifying the center and radius helps you quickly understand its geometric properties.

Explore the circle equation x^2 + y^2 = 1, which describes a circle centered at the origin with a radius of 1. Learn about its geometric properties and applications in mathematics. Suitable for high school students.

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