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Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y + 6 + 4x - 8y.

 Jun 11, 2022
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Rearrange  as

 

x^2   - 6x   +  y^2 + 14y =   6           complete the square on  x, y

 

(x^2 - 6x + 9)  + ( y^2 + 14y +  49 )  =   6 + 9 + 49

 

(x -3)^2  +  ( y + 7)^2  =  64

 

This is a  circle centered at  ( 3 , -7)   with a radius of 8

 

The area enclosed =    pi * 8^2  =     64 pi    units^2

 

 

cool cool cool

 Jun 11, 2022

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