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What is the distance between the center of the circle with equation \(x^2+y^2=6x-8y+24 \) and the point (-3,-12)?

 Oct 10, 2019
 #1
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Rearrange the given equation as

 

x^2 - 6x + y^2 + 8y  = 24     complete the square on x and y

 

x^2 - 6x + 9  + y^2 + 8y + 16  =  24  + 9 + 16

 

(x -3)^2  + (y + 4)^2  =  49

 

The center of the circle  is  ( 3, -4)

 

So.....the distance between the center  and (-3, -12)   is given by :

 

sqrt [ (-3 - 3)^2  + (-12 - - 4)^2 ] =

 

sqrt  [ (-6)^2  + (-8)^2 ] =

 

sqrt [ 36 + 64 ] =

 

sqrt (100) =

 

10 units

 

 

cool cool cool

 Oct 10, 2019

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