SOLUTION: Find an equation of the circle whose diameter has endpoints (1, -5) and (5, -1)

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Question 726654: Find an equation of the circle whose diameter has endpoints (1, -5) and (5, -1)
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(1, -5) and (5, -1)
the mid point is the co ordinates of the center
x=(1+5)/2 =3
y=(-5-1)/2=-3
center(3,-3)
radius =+sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29
(3,-3)(5, -1)
radius =+sqrt%28%285-3%29%5E2%2B%28-1%2B3%29%5E2%29
=sqrt%284%2B4%29
=2sqrt%282%29
Equation of circle
%28x-3%29%5E2%2B%28y%2B3%29%5E2=8

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the circle whose diameter has endpoints (1, -5) and (5, -1)
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Standard form of equation for a circle: %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2, (h,k)=(x,y) coordinates of center, r=radius
use distance formula to find diameter of circle:
diameter=√[(x1-x2)^2+(y1-y2)^2]=√[(5-1)^2+(-1+5)^2]=√[(4)^2+(4)^2]=√32=4√2
radius=2√2
radius^2=8
use end points to find coordinates of center:
midpoint of diameter: (x1+x2)/2, (y1+y2)/2=(5+1)/2, (-1-5)/2=(3,-3)
center: (3,-3)
Equation of given circle: %28x-3%29%5E2%2B%28y%2B3%29%5E2=8