Questions: Find the center-radius form of the equation of the circle with center (0,0) and radius 11. The center-radius form of the equation of the circle is (Type an equation.)

Find the center-radius form of the equation of the circle with center (0,0) and radius 11. The center-radius form of the equation of the circle is (Type an equation.)
Transcript text: Find the center-radius form of the equation of the circle with center $(0,0)$ and radius 11. The center-radius form of the equation of the circle is $\square$ (Type an equation.)
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Solution

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Solution Steps

To find the center-radius form of the equation of a circle, we use the formula \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center \((0,0)\) and radius \(11\), we can substitute these values into the formula.

Step 1: Identify the Given Values

We are given the center of the circle \((h, k) = (0, 0)\) and the radius \(r = 11\).

Step 2: Use the Center-Radius Form of the Circle Equation

The center-radius form of the equation of a circle is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \]

Step 3: Substitute the Given Values into the Equation

Substituting \(h = 0\), \(k = 0\), and \(r = 11\) into the equation, we get: \[ (x - 0)^2 + (y - 0)^2 = 11^2 \]

Step 4: Simplify the Equation

Simplifying the equation, we obtain: \[ x^2 + y^2 = 121 \]

Final Answer

\(\boxed{x^2 + y^2 = 121}\)

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