Answer: [tex](x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16 \lparen option B\rparen}[/tex]
Explanation:
Given:
center of the circle = (3, -2)
radius = 4
To find:
the standard form of the equation of a circle
The standard form of the equation of circle is given as:
[tex]\begin{gathered} (x\text{ - h\rparen}^2\text{ + \lparen y - k\rparen}^2\text{ = r}^2 \\ center\text{ = \lparen h, k\rparen} \end{gathered}[/tex][tex]\begin{gathered} h\text{ = 3, k = -2, r = 4} \\ \\ substitute\text{ the values into the formula:} \\ (x\text{ - 3\rparen}^2\text{ + \lparen y - \lparen-2\rparen\rparen}^2\text{ = 4}^2 \\ (x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16} \end{gathered}[/tex]
The equationof the circle in standard form:
[tex](x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16 \lparen option B\rparen}[/tex]
