CramX Logo

Q
QuestionMathematics

Write the standard form of the equation of the circle with the given characteristics. Center: (0, 0); Radius: 2
12 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

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