Answer:
(x-2)^2 + (y+3)^2 = 5.1^2
Explanation:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where h and k are the x and y values of the center of the circle respectively and r stands for the radius.
The center is given to us, at (2, -3) so we can plug that in:
(x-(2))^2 + (y- (-3))^2 = r^2
Simplify:
(x-2)^2 + (y+3)^2 = r^2
We can also solve for the radius by getting another point given to us: (3,2).
Using the pythagorean theorem, we can find how far the two points are away from each other:
a^2 + b^2 = c^2
1^2 + 5^2 = c^2
1 + 25 = c^2
26 = c^2
c ~ 5.1
Plug the radius we solved for in for r:
(x-2)^2 + (y+3)^2 = 5.1^2