Find the center and radius of the circle. \[ x^{2}+y^{2}=81 \] center \( (x, y)=( \)

To find the **center** and **radius** of the circle given by the equation: \[ x^{2} + y^{2} = 81 \] we can compare it to the standard form of a circle's equation: \[ (x - h)^{2} + (y - k)^{2} = r^{2} \] where: - \((h, k)\) is the **center** of the circle. - \(r\) is the **radius** of the circle. ### Step-by-Step Solution: 1. **Identify the Standard Form Components:** The given equation is: \[ x^{2} + y^{2} = 81 \] This can be rewritten as: \[ (x - 0)^{2} + (y - 0)^{2} = 9^{2} \] Here, it's clear that: - \(h = 0\) - \(k = 0\) - \(r^{2} = 81\) ⇒ \(r = \sqrt{81} = 9\) 2. **Determine the Center and Radius:** - **Center \((h, k)\):** \((0, 0)\) - **Radius \(r\):** \(9\) ### **Final Answer:** - **Center:** \((0, 0)\) - **Radius:** \(9\)