QQuestionMathematics
QuestionMathematics
Write the standard form of the equation of the circle with the given characteristics.
Center: (0, 0); Radius: 2
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Answer
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Step 1:I'll solve this step-by-step using the standard form of a circle equation.
Step 2:: Recall the Standard Form of a Circle Equation
x^{2} + y^{2} = r^{2}
The standard form of a circle equation is: For a circle centered at the origin (0, 0), this simplifies to:
Step 3:: Identify the Given Information
- Center: $$(0, 0)
- Radius: 2
Step 4:: Substitute the Radius into the Equation
Since the radius is $$2$$, we know that $$r^{2} = 4
Step 5:: Write the Final Equation
x^{2} + y^{2} = 4
Final Answer
Key Insights: - When a circle is centered at the origin, its equation is very simple - The radius squared directly appears on the right side of the equation - This equation represents all points (x, y) that are exactly 2 units from the origin
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