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What is the area of the region defined by the equation \(x^2+y^2 - 7 = 2y-8x+1?\)

 Feb 10, 2021
 #1
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+1

Re-arrange:

x^2 +8x         +  y^2 - 2y      =    8                                   complete the squares for x and y

(x+4)^2         +   (y-1)^2      =     8   +  16     +1

(x+4)2             +  (y-1)2           = 52                                              this is circle equation with radius = 5

 

pi r2 = area of circle 

pi 52  25 pi   units2             ( 78.54  units2)

 Feb 10, 2021
 #2
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+1

x^2 + y^2 =  - 7 =  2y  - 8x  + 1

 

x^2 + 8x + y^2 - 2y  =  7 + 1        complete the square on  x and y

 

x^2  + 8x  + 16   +  y^2  - 2y + 1  =  7 + 1 + 16  +  1

 

(x + 4)^2   + ( y - 1)^2  =  25

 

This is a  circle  centered at  ( -4, 1)   with a radius  of  5

 

The  area =  pi 5^2   =  25 pi

 

 

cool cool cool

 Feb 10, 2021

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