Solution
Step 1:
To find the equation of a circle when you know the radius and center, use the formula.
[tex](x\text{ - a\rparen}^2\text{ + \lparen y - b\rparen}^2\text{ = r}^2[/tex]
Where (a, b) represents the center of the circle, and r is the radius. This equation is the same as the general equation of a circle, it's just written in a different form.
Step 2
[tex]\begin{gathered} (x\text{ + 1\rparen}^2\text{ + \lparen y - 3\rparen}^2\text{ = 9} \\ \\ (x\text{ + 1\rparen}^2\text{ + \lparen y - 3\rparen}^2\text{ = 3}^2 \\ \\ a\text{ = -1, b = 3, r = 3} \\ \\ Center\text{ = \lparen-1, 3\rparen and radius r = 3} \end{gathered}[/tex]
Final answer
Center = (-1 , 3)
Radius r = 3
