The equation of the graphed circle is [tex](x - 5)^2 + (y - 2)^2 =25[/tex]
The given parameters are:
- Center: (a,b) = (5,2)
- Point: (x,y) = (9,5)
Radius
Start by calculating the radius of the circle using the following distance formula
[tex]r = \sqrt{(x -a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(9 -5)^2 + (5 - 2)^2}[/tex]
[tex]r = \sqrt{25}[/tex]
Square both sides of the equation
[tex]r^2 = 25[/tex]
Circle Equation
The equation of the circle is then calculated using:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Substitute values for (a,b)
[tex](x - 5)^2 + (y - 2)^2 = r^2[/tex]
Also, substitute 25 for r^2
[tex](x - 5)^2 + (y - 2)^2 =25[/tex]
Hence, the equation of the graphed circle is [tex](x - 5)^2 + (y - 2)^2 =25[/tex]
Read more about circle equations at:
https://brainly.com/question/1559324
