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The line y = 3x - 8 intersects the circle x^2 + (y - 1)^2 = 10 at A and B.  Find the midpoint of AB.  Enter your answer in the form (x,y).

 Apr 12, 2022
 #1
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y  =3x + 8

 

So

 

x^2  + [ 3x +8 -1]^2   = 10

 

x^2 + [3x + 7]^2   =10

 

x^2 + 9x^2 + 42x + 49  =10

 

10x^2 + 42x + 39  = 0

 

The sum of the two solutions to this   =   -42 /10   = -4.2

 

The x  midpoint  of  these two solutions =  [sum of two solutions / 2 ] =  (-4.2 / 2 )  =   -2.1

 

And the y coordinate of this midpoint is  3(-2.1) + 8 =  1.7

 

(x,y) =  ( -2.1 , 1.7)   

 

cool cool cool

 Apr 12, 2022

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