\begin{tabular}{l|l|} estion list & \multicolumn{1}{l}{\( \begin{array}{l}\text { A circle has the equation } x^{2}+y^{2}-3 x-6 y+9=0 . \\ \text { (a) Find the center (h,k) and radius r of the circle. } \\ \text { (b) Graph the circle. } \\ \text { (c) Find the intercepts, if any, of the graph. }\end{array} \)} \\ Question 7 & \( \begin{array}{l}\text { (a) The center of the circle is }\left(\frac{3}{2}, 3\right) . \\ \text { (Type an ordered pair, using integers or fractions.) } \\ \text { Question } 8 \\ \text { Que radius of the circle is unknown. } \\ \text { (Type an integer or a fraction.) }\end{array} \) \\ \hline\end{tabular}

The equation of the circle can be rewritten in standard form by completing the square. Here, you rearrange \( x^{2} - 3x \) and \( y^{2} - 6y \) to get \((x - \frac{3}{2})^2 + (y - 3)^2 = \frac{9}{4}\). This reveals that the center of the circle is \(\left(\frac{3}{2}, 3\right)\) and its radius is \(\frac{3}{2}\). To graph the circle, start with the center at \(\left(\frac{3}{2}, 3\right)\) and then draw a circle with a radius extending \(\frac{3}{2}\) units in all directions. For intercepts, plug \(y = 0\) into the circle's equation to find the x-intercepts, and \(x = 0\) for y-intercepts, solving these will yield the points where the circle intersects the axes, if at all!