The general structure of the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
Note that the equation has minus signs inside the parentheses, this means that the sign of the coordinates is the opposite as the one shows on the equation.
The first step is to identify the coordinates of the center of the circle in each equation as well as the radius:
Equation 1:
[tex](x-3)^2+(y+2)^2=9[/tex]
The x-coordinate of the center is the value inside the first parentheses: h= 3
The y-coordinate of the center is the value inside the second parentheses: k= -2
[tex]center\colon(3,-2)[/tex]
To determine the radius you have to calculate the square root of the last number of the equation:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]
Use the same logic for the other three equations:
Equation 2:
[tex](x-3)^2+(y-2)^2=16[/tex]
h=3
k=2
[tex]\text{center:(3,2)}[/tex]
Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]
Equation 3
[tex](x+3)^2+(y+2)^2=16[/tex]
h=-3
k=-2
[tex]\text{center:(-3,-2)}[/tex]
Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]
Equation 4
[tex](x-3)^2+(y-2)^2=9[/tex]
h=3
k=2
[tex]\text{center:(3,2)}[/tex]
Radius:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]
Next, you have to determine the center and the radius of each graph:
Circle 1:
Has a radius with a length of 4 units and center (3,2), the equation that corresponds to this circle is the second equation.
Circle 2:
Has a radius with a length of 4 units and the center at (-3,-2), the equation that corresponds to this circle is the third equation.
Circle 3:
Has a radius with a length of 3 units and a center at (3,2), the equation that corresponds to this circle is the fourth equation.
Circle 4:
Has a radius with a length of 3 units and center at (3,-2), the equation that corresponds to this graph is the first equation.
