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.