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# help

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ggghhhhhhhhhhhhhh

Nov 18, 2019
edited by shgg111  Nov 18, 2019

#1
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Using the equation  of the line

2x + 3y  = 3

3y = 3  - 2x

y =  (3 - 2x)  /3

Let  the center of the circle be  ( x, (3 -2x) / 3  )

And  the distance from this center  to both of the given  points is  equal ....so...

(x -8)^2  + [ (3 -2x)/3  + 5]^2   =   ( x + 1)^2 + [ (3 -2x)/3 -4 ] ^2    simplify

x^2 - 16x + 64  +  [ (18 -2x)/ 3 ]^2  =  x^2 + 2x + 1 +  [ (-9 - 2x) / 3 ] ^2

x^2 - 16x+ 64 + [ 324 - 72x + 4x^2/] /9  = x^2 + 2x + 1  + [ 81 + 36x + 4x^2 ] / 9

-16x + 64  + [ 324 - 72x + 4x^2 ] / 9  =  2x + 1 + [81  +36x+ 4x^2]/9      multiply through by 9

-144x + 576 + 324 - 72x + 4x^2 =  18x + 9 + 81 + 36x + 4x^2

-216x + 900 = 90 + 54x

810  = 270 x     divide both sides by 270

3  = x

And using the equation of the line     y = [ 3 - 2(3)] / 3  = -1

So...the center of the circle is  (3 , -1)

And using either point and this center, we can find r^2  as

(8 - 3)^2 + ( -5 + 1)^2  = r^2

5^2 + (-4)^2 = r^2

41  = r^2

So...the eqaution is  ( x - 3)^2 + ( y + 1)^2  =  41

Here's the graph : https://www.desmos.com/calculator/20kbuxcqtc   Nov 18, 2019
#2
+2

thank you

shgg111  Nov 18, 2019