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# Find the center of the circle passing through the points (-1, 0) , (1,0) , and (3,1) . Express your answer in the form '.'

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Find the center of the circle passing through the points (-1, 0), (1,0), and (3,1). Express your answer in the form "."

waffles  Nov 10, 2017
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(-1, 0), (1,0), and (3,1)

Let the center be ( x, y)

So the distance from the center to each point will be the same

So...we have

(x - 1) + y^2  =  (x + 1)^2 + y^2

x^2 - 2x + 1  =  x^2 + 2x + 1

-4x  = 0     so the x coordinate of the center  is    x = 0

And we can find y thusly

(0 -1)^2  + y^2  =  (0 - 3)^2 + (y - 1)^2

1 +  y^2   =  9  + y^2 - 2y + 1

2y =  9   ⇒  y = 9/2  =  4.5

So  the center is  (0, 4.5)

And the radius  is   sqrt ( 1 + 4.5^2)  = sqrt (21.25)

nd the equation of the circle is :   x^2  + (y - 4.5)^2  =  21.25

Here's  a graph : https://www.desmos.com/calculator/puz5c5m6yv

CPhill  Nov 11, 2017

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