A circle has the equation \( x^{2}+y^{2}=36 \). (a) Find the center ( \( \mathrm{h}, \mathrm{k} \) ) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or decimals.)

The center of the circle is (0, 0) and the radius is 6. This is derived from the standard form of a circle's equation, which is \( (x - h)^2 + (y - k)^2 = r^2 \). Here, \( h \) and \( k \) represent the center's coordinates, and since the equation simplifies to \( x^2 + y^2 = 36 \), it indicates the center is at the origin and the radius \( r \) is the square root of 36. For graphing, you would draw a circle centered at the origin with a radius of 6. You can plot points at (6,0), (0,6), (-6,0), and (0,-6) to guide you in creating a perfect circle. To find the intercepts, since the center is at (0,0), both the x-intercepts and y-intercepts are where the circle intersects the axes: x-intercepts at (6,0) and (-6,0), and y-intercepts at (0,6) and (0,-6).