Answer:
[tex]\displaystyle \large{(x-3)^2+(y+7)^2=9}[/tex]
Step-by-step explanation:
By looking at the graph, we can say that the circle has a center point at (3,-7). Next, find the radius which is the distance between center and an endpoint.
Distance Formula
[tex]\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
Determine:
- Center = [tex]\displaystyle \large{(x_2,y_2)}[/tex] = (3,-7)
- Endpoint = [tex]\displaystyle \large{(x_1,y_1)}[/tex] = (0,-7)
Therefore:
[tex]\displaystyle \large{\sqrt{(3-0)^2+(-7-(-7))^2}}\\\\\displaystyle \large{\sqrt{3^2+(-7+7)^2}}\\\\\displaystyle \large{\sqrt{9} = 3}[/tex]
Therefore, radius = 3.
Equation of Circle
[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
- (h,k) = center = (3,-7)
- r = 3 so r² = 9
Hence:
[tex]\displaystyle \large{(x-3)^2+(y-(-7))^2=3^2}\\\\\displaystyle \large{(x-3)^2+(y+7)^2=9}[/tex]
