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An archeologist found the remains of an ancient wheel,which she placed on a grid.If an arc of the wheel passes through A(-8,0),B(-3,4),and C(8,0),locate the center of the wheel,and the standard equation of the circle defining its boundary.

 Dec 3, 2020
 #1
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If we  have  the points  A=  ( -8,0)  and C =   ( 8,0)  on the circle....then AC will form a chord in the  circle

This means that  the center  of  the  circle  will  have  the coordinates  (0,a)

 

And  the distance  from the center  to   B  will be the same distance from   the center to   C

 

So  we have this

 

(-3)^2  + (4-a)^2  =  (8)^2  + ( a)^2 

 

9 +  16  - 8a  + a^2  = 64 +  a^2     simplify

 

-39  = 8a

 

a  =  -39/8

 

The center is  (0, -39/8)

 

The radius ^2  =    ( 8)^2  +  ( -39/8)^2 =   5617/64

 

The equation is

 

x^2  +  ( y + 39/8)^2  = 5617/64

 

  See the graph here :  https://www.desmos.com/calculator/ul4b4frbtz

 

 

cool cool cool

 Dec 3, 2020

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