Part 1 of 4 A circle has the equation \( \mathrm{x}^{2}+\mathrm{y}^{2}=64 \). (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 \( \square \). (Type an ordered pair, using integers or decimals.)

The equation you have, \( \mathrm{x}^{2}+\mathrm{y}^{2}=64 \), represents a circle centered at the origin. The center \( (\mathrm{h}, \mathrm{k}) \) is \( (0, 0) \) and the radius \( r \) is given by the square root of 64, which is 8. Now for part (b), when graphing the circle, you would draw a circle centered at the origin with a radius of 8. You can plot points at a distance of 8 in all directions (up, down, left, right), which gives you points like \( (8, 0) \), \( (-8, 0) \), \( (0, 8) \), and \( (0, -8) \). For discovering the intercepts (part c), the circle intersects the x-axis where \( y = 0 \): \( x^2 + 0^2 = 64 \) leads to \( x = 8 \) and \( x = -8 \). For the y-axis, where \( x = 0 \): \( 0^2 + y^2 = 64 \) gives \( y = 8 \) and \( y = -8 \). So the intercepts are \( (-8, 0) \), \( (8, 0) \), \( (0, 8) \), and \( (0, -8) \).