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The points (0, 4) and (1, 3) lie on a circle whose center is on the x-axis. What is the radius of this circle? (its due today so could you hurry :) ) Please include an explanation so I can learn from it. Thanks so much!      It's due in 5 minutes. Please hurry!!!!!

 Nov 24, 2020
edited by Guest  Nov 24, 2020
 #2
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Notice if the  center is on the  x axis...it must have the coordinates of  (a, 0)

 

Because the  distance  from each point to  the  center is the  same we  can solve for a  thusly :

 

(a-0)^2  + (0 - 4)^2   =  ( a -1)^2  + ( 0 -3)^2    simplify

 

a^2  + 16 = a^2  -2a + 1  + 9     subtract a^2  from both sides

 

16  = -2a + 10

 

16 - 10  = -2a

 

6 = -2a

 

6/-2 =  a

 

-3  = a

 

Coordinates of center=  (-3,0)

 

Radius =  sqrt [ (-3 - 0)^2   + (4 - 0)^2  ]  =  sqrt [ 9 + 16 ] =  sqrt 25  =  5

 

Here's a graph :   https://www.desmos.com/calculator/cu9ityz6lb

 

 

cool cool cool

 Nov 24, 2020
 #3
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Thank you so so so so so so so so much! You're amazing CPhill. A true life saver. Thanks again!!!!

Guest Nov 24, 2020

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