Step 1:
First, write the general equation of a circle
[tex]\begin{gathered} (x-a)^a+(y-b)^2=r^2 \\ r\text{ is the radius} \\ (a,\text{ b) is the center} \end{gathered}[/tex]
Step 2:
Question 1
[tex]\begin{gathered} x^2+y^2\text{ = 121} \\ x^2+y^2=11^2 \\ \text{radius r = 11} \\ \text{center = (0 , 0)} \end{gathered}[/tex]
Question 2
[tex]\begin{gathered} (x-2)^2+y^2\text{ = 64} \\ (x-2)^2+y^2=8^2 \\ \text{Center = (2, 0)} \\ r\text{ = 8} \end{gathered}[/tex]
Question 3
[tex]\begin{gathered} (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = 36} \\ (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = }6^2 \\ \text{Center = (-}\frac{3}{2}\text{ , -}\frac{5}{8}) \\ r\text{ = 6} \end{gathered}[/tex]
Question 4
[tex]\begin{gathered} (x-1)^2+(y+7)^2\text{ = 9} \\ (x-1)^2+(y+7)^2\text{ = }3^2 \\ \text{Center = (1, -7)} \\ r\text{ = 3} \end{gathered}[/tex]
Question 5
[tex]\begin{gathered} (x+8)^2+(y-3)^2\text{ = 7} \\ (x+8)^2+(y-3)^2\text{ = (}\sqrt[]{7})^2 \\ \text{Center = (-8, 3)} \\ \text{radius r = }\sqrt[]{7} \end{gathered}[/tex]
