Give the equation of the circle whose center is (5, -3) and goes through (2,5)

For this we use 
y - y1 = m ( x - x1 ) to help us find the slope first
so we will plug in the given coordinates
5 - -3 = m ( 2 - 5)
8 = m ( -3)
divide by the -3 to isolate the m
-8/3 = m

so now we know that the slope is 11

we will go back to that equation to find the y- intercept
y - y1 = m ( x - x1)
now we will plug in the slope and the first coordinate we are given
so
y - -3 = -8/3 ( x -5)
do the distributive property
y + 3 = -8/3x + 40/3
subtract 3 from both sides to isolate the y
y = -8/3x + 31/3

now to write in standard form
add 8/3x to both sides to bring it to the left of the equation
8/3x + y = 31/3

Hope this helps :)

Add up all the sides