SOLUTION: The equation of a circle where A and B are the endpoints of the diameter Using the points A(4,−9 ) and B(−12,−3 )

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Question 490005: The equation of a circle where A and B are the endpoints of the diameter
Using the points A(4,−9 ) and B(−12,−3 )
Answer by lwsshak3(11628) About Me  (Show Source):
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The equation of a circle where A and B are the endpoints of the diameter
Using the points A(4,−9 ) and B(−12,−3 )
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Standard form of an equation for a circle: (x-h)^2+(y-k)^=r^2, (h,k) being (x,y) coordinates of the center and r=radius
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Using distance formula to find diameter of circle:
d=√[(x1-x2)^2+(y1-y2)^2]
d=√[(-12-4)^2+(-3-(-9))^2]
d=√[(-16)^2+(6)^2]
d=√(256+36)=√292
r=d/2=√292/2
r^2=292/4=73
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Using midpoint formula to find coordinates of the center:
(x1+x2)/2,(y1+y2/2=(-12+4)/2,(-3+(-9))/2=(-4,-6)
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Equation:
(x+4)^2+(y+6)^2=73