\( 1 \leftarrow \left\lvert\, \begin{array}{l}\text { A circle has the equation } x^{2}+y^{2}-3 x-6 y+9=0 . \\ \text { (a) Find the center (h,k) and radius } r \text { of the circle. } \\ \text { (b) Graph the circle. } \\ \text { (c) Find the intercepts, if ahy, of the graph. } \\ \begin{array}{l}\text { (a) The center of the circle is } \\ \text { (Type an ordered pair, using integers or fractions.) }\end{array}\end{array}\right. \)

To find the center and radius of the given circle equation \( x^{2}+y^{2}-3x-6y+9=0 \), we can rewrite it in standard form. Completing the square for the \( x \) and \( y \) terms, we get \( (x - \frac{3}{2})^2 + (y - 3)^2 = \frac{9}{4} \). Thus, the center is \( \left(\frac{3}{2}, 3\right) \) and the radius \( r \) is \( \frac{3}{2} \). Now, when graphing the circle, start by plotting the center \( \left(\frac{3}{2}, 3\right) \). From this point, draw a circle that extends \( \frac{3}{2} \) units in all directions. For the intercepts, set \( y = 0 \) to find the x-intercepts and set \( x = 0 \) for the y-intercepts. Solving these will provide points where the circle crosses the axes.