To begin, let's recall the Distance Formula. It is used to find the distance d between two points (x_1,y_1) and (x_2,y_2).
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
We will find the radius of our circle by substituting its center and one point through which the circle passes into this formula and finding the distance between these two points. Let's look at the graph to identify the coordinates of these points.
The center has the coordinates (2,2). We can also tell that the circle passes through the point (2,6). Now we are ready to use the Distance Formula. Let's do it!
Let's now recall the standard form of an equation of a circle.
(x- h)^2+(y- k)^2= r^2
In this formula, ( h, k) is the center of the circle and r is its radius. We have already found that the center of the circle is ( 2, 2). This information, together with r= 4, is enough to write the equation.
(x- 2)^2+(y- 2)^2= 4^2
⇕
(x-2)^2+(y-2)^2=16
