coordinates

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

                                      x² + y²  =  2x – 6y + 6 + 4x – 8y    

rearrange & group         (x² – 6x    ) + (y² + 14y    )  =  6    

Complete the squares on x and y.  Add the same amount to the right side that you add to the left.    

                                           (x² – 6x + 9) + (y² + 14y + 49)  =  6 + 9 + 49    

                                           (x – 3)² + (y + 7)²  =  64    

That's a circle in the form   (x – h)² + (y –k)² = r²  where h and k locate the center and r is the radius.    

Area of the circle is A = π r²     ——>>  A = 64 π  =  201.06    

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