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Find the center of the circle that passes through the points (1,3), (3,-2), (5,3).

 Nov 11, 2019
 #1
avatar+19773 
+2

Using the formula for a circle   (x-h)^2 + (y-k)^2 = r ^2

 

for the first point this becomes   (1-h)^2 + (3-k)^2 = r^2

for the second point , this becomes  (3-h)^2 +(-2-k)^2 = r^2     these are both equal to r^2, so equate them

    then expand, collect 'like' terms and simplify to

4h-10k-3=0   (1)

 

Do all of this to the THIRD set of points and equate to the second set of points (red above)

   expand and simlify to

4h+10k-21 =0     (2)

 

solve (1) and (2) for h,k    =   3, 9/10

     then use distance formula from the center (3,9/10)  to any of the three points to find r^2 = 8.41  

 

(x-3)^2 + (y-9/10)^2 = 8.41

 Nov 11, 2019
edited by ElectricPavlov  Nov 11, 2019
 #2
avatar+19773 
+2

Here is desmos graph

https://www.desmos.com/calculator/h99cfiuvht

 Nov 11, 2019

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