Sketch the graph of the curve with equation x² + y²= 1

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 \(r\).

Learn how to graph the circle with the equation x² + y² = 1. This problem explains key concepts such as the center, radius, and symmetry of the circle in coordinate geometry. Suitable for students in Grades 9-10.

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