Find the intercepts of the circle. \[ (x-2)^{2}+(y+7)^{2}=9 \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The \( x \)-intercept(s) is/are (Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.)

To find the intercepts of the circle given by the equation \[ (x-2)^{2}+(y+7)^{2}=9, \] we will first find the \( x \)-intercepts by setting \( y = 0 \) and solving for \( x \). 1. Substitute \( y = 0 \) into the equation: \[ (x-2)^{2} + (0 + 7)^{2} = 9. \] This simplifies to: \[ (x-2)^{2} + 49 = 9. \] 2. Rearranging gives: \[ (x-2)^{2} = 9 - 49, \] \[ (x-2)^{2} = -40. \] Since the left side is a square and the right side is negative, there are no real solutions for \( x \). Therefore, there are no \( x \)-intercepts. Next, we will find the \( y \)-intercepts by setting \( x = 0 \) and solving for \( y \). 1. Substitute \( x = 0 \) into the equation: \[ (0 - 2)^{2} + (y + 7)^{2} = 9. \] This simplifies to: \[ 4 + (y + 7)^{2} = 9. \] 2. Rearranging gives: \[ (y + 7)^{2} = 9 - 4, \] \[ (y + 7)^{2} = 5. \] 3. Taking the square root of both sides: \[ y + 7 = \pm \sqrt{5}. \] 4. Solving for \( y \): \[ y = -7 + \sqrt{5} \quad \text{and} \quad y = -7 - \sqrt{5}. \] Thus, the \( y \)-intercepts are: \[ \left(0, -7 + \sqrt{5}\right) \quad \text{and} \quad \left(0, -7 - \sqrt{5}\right). \] In conclusion, the intercepts of the circle are: - \( x \)-intercepts: None - \( y \)-intercepts: \( \left(0, -7 + \sqrt{5}\right), \left(0, -7 - \sqrt{5}\right) \) So, the final answer for the \( x \)-intercepts is: **A. The \( x \)-intercept(s) is/are: None**.