a. Type the equation in center-radius form. \( (x-5)^{2}+(y-4)^{2}=9 \) (Simplify your answer.) b. Type the equation in general form. (Simplify your answer.)

a. The equation you provided is already in center-radius form, which is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((h, k)\) is the center of the circle and \(r\) is the radius. In your equation: \[ (x - 5)^{2} + (y - 4)^{2} = 9 \] The center of the circle is \((5, 4)\) and the radius \(r\) is \(\sqrt{9} = 3\). So, the center-radius form is: \[ (x - 5)^{2} + (y - 4)^{2} = 9 \] b. To convert the equation to general form, we need to expand and simplify it. Starting with: \[ (x - 5)^{2} + (y - 4)^{2} = 9 \] Expanding both squares: \[ (x^2 - 10x + 25) + (y^2 - 8y + 16) = 9 \] Combining like terms: \[ x^2 - 10x + y^2 - 8y + 25 + 16 = 9 \] This simplifies to: \[ x^2 - 10x + y^2 - 8y + 41 = 9 \] Now, subtract 9 from both sides: \[ x^2 - 10x + y^2 - 8y + 32 = 0 \] Thus, the general form of the equation is: \[ x^2 - 10x + y^2 - 8y + 32 = 0 \]