Answer:
See attachment.
Step-by-step explanation:
The given equation (x - 2)² + (y - 1)² = 9 is in the standard form of the equation of a circle.
The general equation of a circle is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{General equation of a circle}}\\\\(x-h)^2+(y-k)^2=r^2\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$(h, k)$ is the center.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius.}\end{array}}[/tex]
Therefore, in this case:
So, the center of the circle is located at point (2, 1).
To find the radius (r), take the square root of 9:
[tex]\sqrt{r^2}=\sqrt{9}\\\\r=3[/tex]
Therefore, the radius of the circle is r = 3.
To graph the circle, begin by plotting the center at point (2, 1).
Since the radius of the circle is 3, this means the distance from the center to any point on the circle is 3 units.
Points that are 3 units up and down from the centre are:
[tex](2, 1 + 3) = (2, 4)\\\\(2, 1-3) = (2, -2)[/tex]
Points that are 3 units left and right from the center are:
[tex](2 - 3, 1) = (-1, 1)\\\\(2 + 3, 1) = (5,1)[/tex]
Therefore, plot points (2, 4), (2, -2), (-1, 1) and (5, 1), and connect these points to form the circle.
