1. **Find the equation of the circle given the center and radius or diameter.** The general equation of a circle with center $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ If the diameter $d$ is given, then radius $r = \frac{d}{2}$. --- **Problem 1:** Center at origin $(0,0)$, radius $16$. Equation: $$ (x - 0)^2 + (y - 0)^2 = 16^2 $$ $$ x^2 + y^2 = 256 $$ --- **Problem 2:** Center $(0,0)$, radius $8.56$. Equation: $$ x^2 + y^2 = 8.56^2 = 73.2736 $$ --- **Problem 3:** Center $(0,0)$, diameter $36$. Radius: $$ r = \frac{36}{2} = 18 $$ Equation: $$ x^2 + y^2 = 18^2 = 324 $$ --- **Problem 4:** Center $(0,0)$, diameter $22.33$. Radius: $$ r = \frac{22.33}{2} = 11.165 $$ Equation: $$ x^2 + y^2 = 11.165^2 = 124.66 $$ --- **Problem 5:** Center $(8,10)$, radius $3$. Equation: $$ (x - 8)^2 + (y - 10)^2 = 3^2 = 9 $$ --- **Problem 6:** Center $(2,-3)$, diameter $9$. Radius: $$ r = \frac{9}{2} = 4.5 $$ Equation: $$ (x - 2)^2 + (y + 3)^2 = 4.5^2 = 20.25 $$ --- **Summary of equations:** 1. $x^2 + y^2 = 256$ 2. $x^2 + y^2 = 73.2736$ 3. $x^2 + y^2 = 324$ 4. $x^2 + y^2 = 124.66$ 5. $(x - 8)^2 + (y - 10)^2 = 9$ 6. $(x - 2)^2 + (y + 3)^2 = 20.25$