Find equation of the circle whose diameter has endpoints (1,-6) and (-9,0)

We need to find the midpoint of these two points......that will be the center of the circle......then, we can use the distance formula to find the distance between the center and one of the points.....this will give us the radius

Midpoint   =   [   ( 1 - 9 ) / 2  , ( -6 + 0) / 2 ]  =  [  -8/2 , -6/2]  =  [ -4, -3 ]  ......this is the center

Distance between   [-4, -3]   and  [-9, 0]  = radius  = √ ( [ -4 + 9]^2 + [-3 - 0]^2 )  =

√ [ 5^2  + (-3)^2 ]  = √ [25  + 9]  = √34

So the equation is :

( x + 4)²   + ( y + 3)²  =  34