Subjects algebra

Circle Equation 59Ec35

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1. **Stating the problem:** We are given the equation $$\sqrt{x^2 + y^2} = 1$$ which represents a graph. 2. **Understanding the formula:** The expression $$\sqrt{x^2 + y^2}$$ represents the distance from the point $$(x,y)$$ to the origin $$(0,0)$$ in the Cartesian plane. 3. **Interpreting the equation:** The equation $$\sqrt{x^2 + y^2} = 1$$ means all points $$(x,y)$$ whose distance from the origin is exactly 1. 4. **Simplifying the equation:** Square both sides to remove the square root: $$ (\sqrt{x^2 + y^2})^2 = 1^2 $$ which simplifies to $$ x^2 + y^2 = 1 $$ 5. **Conclusion:** This is the standard equation of a circle centered at the origin with radius 1. Therefore, the graph represents a circle centered at $$(0,0)$$ with radius $$1$$.