Answer: [tex](x\text{ + 1\rparen}^2\text{ + \lparen y - 2\rparen}^2\text{ = 9}[/tex]
Explanation:
Given:
A circle on a coordinate plane with a dot representing the center
To find:
Equation of the circle
The formula for the equation of a circle is given as:
[tex]\begin{gathered} (x\text{ - h\rparen}^2+\text{ \lparen y - k\rparen}^2\text{ = r}^2 \\ where\text{ center = \lparen h, k\rparen} \\ radius\text{ = r} \end{gathered}[/tex]
Identifying the coordinate of the center and the unit for the radius:
Center (h, k) = (-1, 2)
h = -1, k = 2
radius = 3 units from the center to the circumference
r = 3
substitute the values into the formula:
[tex]\begin{gathered} (x\text{ - \lparen-1\rparen\rparen}^2\text{ + \lparen y - 2\rparen}^2=\text{ 3}^2 \\ \\ The\text{ equation:} \\ (x\text{ + 1\rparen}^2\text{ + \lparen y - 2\rparen}^2\text{ = 9} \end{gathered}[/tex]
