The equation of a circle is the equation that represents the circle on the coordinate plane
The equation of the circle is [tex](x +3)^2 + (y -6)^2 = 13[/tex]'
From the attached figure, we have the following parameters:
- Center: (a,b) = (-3, 6)
- Point on the circumference: (x,y) = (0,8)
Start by calculating the radius r using the following distance formula
[tex]d = \sqrt{(x -a)^2 +(y - b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(0 --3)^2 +(8 - 6)^2}[/tex]
[tex]r = \sqrt{9 +4}[/tex]
[tex]r = \sqrt{13}[/tex]
Square both sides
[tex]r^2 = 13[/tex]
The equation of the circle is then calculated as:
[tex](x - a)^2 + (y -b)^2 = r^2[/tex]
Substitute values for a and b
[tex](x - -3)^2 + (y -6)^2 = r^2[/tex]
This gives
[tex](x +3)^2 + (y -6)^2 = r^2[/tex]
Substitute [tex]r^2 = 13[/tex]
[tex](x +3)^2 + (y -6)^2 = 13[/tex]
Hence, the equation of the circle is [tex](x +3)^2 + (y -6)^2 = 13[/tex]'
Read more about circle equations at:
https://brainly.com/question/1559324
