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Points (-1,-3) and (5,1) are the endpoints of a diameter of a circle.  What is the equation of the circle?

 Dec 16, 2019
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Hello wiseowl! 

 

The diameter must pass through the midpoint of the circle. Furthermore, the midpoint of the diameter is the center of the circle. 

Therefore, from the diameter, we can find the radius length and center, finding the equation in the end. 

 

The midpoint of (-1,-3) and (5,1) is \((\frac{-1+5}{2},\frac{-3+1}{2})\) or \((2,-1)\).

 

The diameter length is \(\sqrt{(5-(-1))^2+(1-(-3))^2}=2\sqrt{13}\)

Then the radius must be \(\sqrt{13}\)

 

The equation of the circle must be \((x-2)^2+(y+1)^2=13\)

 

I hope this helped, 

 

Gavin

 Dec 16, 2019
edited by GYanggg  Dec 16, 2019

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