Answer:
[tex]\displaystyle \large{(x-5)^2+(y-2)^2=25}[/tex]
Step-by-step explanation:
Given:
- Center = (5,2)
- Endpoint = (8,6)
First, find radius via distance between center and endpoint. The formula of distance between two points is:
[tex]\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
Determine:
- [tex]\displaystyle \large{(x_1,y_1)=(5,2)}[/tex]
- [tex]\displaystyle \large{(x_2,y_2)=(8,6)}[/tex]
Hence:
[tex]\displaystyle \large{\sqrt{(8-5)^2+(6-2)^2}}\\\displaystyle \large{\sqrt{(3)^2+(4)^2}}\\\displaystyle \large{\sqrt{9+16} = \sqrt{25} = 5}[/tex]
Therefore, the radius is 5.
Then we can substitute center and radius in circle equation. The equation of a circle is:
[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]
Our center is at (h,k) which is (5,2) and radius beings 5.
Hence, your answer is:
[tex]\displaystyle \large{(x-5)^2+(y-2)^2=25}[/tex]
