Given: The graph of the circle shown in the image
To Determine: The equation of the given circle
Solution
The general equation of a circle given the center and the radius is as shown below
[tex]\begin{gathered} Equation(circle):(x-a)^2+(y-b)^2=r^2 \\ Where \\ Center=(a,b) \\ radius=r \end{gathered}[/tex]
Let us determine the center and radius of the given circle as shown below
It can be observed that
[tex]\begin{gathered} Center=(a,b)=(-4,4) \\ radius(r)=3units \end{gathered}[/tex]
Let us substitute the center and the radius into the equation
[tex]\begin{gathered} Equation(circle):(x-a)^2+(y-b)^2=r^2 \\ a=-4 \\ b=4 \\ r=3 \\ Equation(circle)=(x+4)^2+(y-4)^2=3^2 \\ =(x+4)^2+(y-4)^2=9 \end{gathered}[/tex]
Hence, the equation of the circle is
(x + 4)² + (y - 4)² = 9
