Answer:
(x-1)² + (y-6)² = 4
Step-by-step explanation:
From the circle, endpoints (horizontal) are (-1,6) and (3,6). We will use these points to find midpoint (center) of the circle.
Midpoint Formula:
[tex]\displaystyle \large{\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right )}[/tex]
Determine:
- [tex]\displaystyle \large{(x_1,y_1) = (-1,6)}[/tex]
- [tex]\displaystyle \large{(x_2,y_2)=(3,6)}[/tex]
Hence:
[tex]\displaystyle \large{\left(\dfrac{-1+3}{2}, \dfrac{6+6}{2}\right )}\\\displaystyle \large{\left(\dfrac{2}{2} , \dfrac{12}{2}\right )}\\\displaystyle \large{\left( 1 ,6\right )}[/tex]
The midpoint (center) is (1,6). Next, find the radius which can be found by finding the distance between center and endpoint.
Determine:
- Center = (1,6) = (x1,y1)
- Endpoint = (3,6) = (x2,y2)
Distance Formula:
[tex]\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
Therefore:
[tex]\displaystyle \large{\sqrt{(3-1)^2+(6-6)^2}}\\\displaystyle \large{\sqrt{2^2}}\\\displaystyle \large{\sqrt{4} = 2}[/tex]
So our radius = 2.
Now we have:
Equation of Circle:
[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]
Where (h,k) is a center and r is radius:
Therefore, the solution is [tex]\displaystyle \large{(x-1)^2+(y-6)^2=4}[/tex]
Attachment is added for visual reference.
