is the equation of the required circle.
Step-by-step explanation:
Step 1 :
Let A = (8,-9) and B = (6,-3) be the endpoints of the diameter of the given circle.
We need to determine the circle's equation with this diameter
Step 2 :
The mid point of the diameter will be center of the required circle.
Let M = (x,y) be the mid point of the circle.
So we have x = (8+6)÷ 2 , y = ((-9) + (-3)) ÷ 2
M = ( 7, -6) is the midpoint of the diameter and the center of the circle.
Step 3 :
The radius of the circle is distance between midpoint and any one of the end point of the diameter that is distance between point A(8,-9) and M ( 7,-6)
Distance between the 2 points
is given by

So distance between A(8,-9) and M ( 7,-6) = 
= 
Hence the radius r is 
Step 4 :
The equation of circle with center (a,b) = (7,-6) and radius r =
is given by

=>
=>
is equation of the required circle.
Step 5 :
Answer :
is equation of the required circle.