Find the equation of the circle centered at (2,2) and passing through (4,5).
The general equation for any circle uses this:
(x-h)^2 + (y-k)^2 = r^2 with (h, k) being the center and r being the radius.
We already know what the center is, so now all we need to do is find the radius. we can easily find the radius with the pythagorean theorem.
We can imagine a right triangle with the radius from (2, 2) to (4, 5) as the hypotenuse.
Let's look for the legs first. 4-2=2. The second leg is 5-2=3.
2^2 + 3^2 = square root of 13
We can bring r^2 and (h,k) into the general equation.
The equation you are looking for is (x-2)^2 + (y-2)^2 = 13
I hope this helps.