If (8, −9) and (6, −3) are the endpoints of the diameter of a circle, what is the equation of the circle?

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.