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What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?

 Aug 10, 2024
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Re-arrange by simplifying to :  

x^2 +12x       +y^2   +2y    =   10        Now complete the squares for x and y 

x^2 + 12x +36    +   Y^2  +2y +1    = 10  +36 + 1 

(x+6)^2       + ( y+1)^2  =   47             47 is r^2   For this circle 

         Area of a circle = pi r^2   = pi * 47 = 47*pi = 147.65  units^2 

 Aug 10, 2024

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