The equation $x^2 + y^2 = 1$ represents a circle in the coordinate plane. Here's how to sketch its graph:

1. Center: The equation is in standard form for a circle, $x^2 + y^2 = r^2$, where $r$ is the radius, and the center is at $(0, 0)$. In this case, the center is at the origin $(0, 0)$.

2. Radius: The radius of the circle is $r = 1$, as $r^2 = 1$.

3. Key Points:

   • The circle will intersect the x-axis at $(1, 0)$ and $(-1, 0)$.
   • The circle will intersect the y-axis at $(0, 1)$ and $(0, -1)$.

4. Symmetry: The circle is symmetric with respect to both the x-axis and the y-axis.

To sketch:

• Draw a point at the center $(0, 0)$.
• Mark points at $(1, 0)$, $(-1, 0)$, $(0, 1)$, and $(0, -1)$.
• Connect these points in a smooth, round curve to complete the circle.

Would you like a detailed graph image for this curve?

5 Related Questions:

1. How do you find the equation of a circle with a different radius?
2. What are the properties of a circle on the coordinate plane?
3. How can you translate the circle to a different center?
4. How does changing the radius affect the graph of the circle?
5. What are the parametric equations of a circle?

Tip:

For any general circle equation $(x - h)^2 + (y - k)^2 = r^2$, the center is at $(h, k)$ and the radius is $r$.