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Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+4x-4y+12

 Sep 6, 2024
 #1
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Re-arrange as

x^2 -6x       +  y^2 +10y    = 18     Complete the square for x and y 

(x-3)^2       +   (y+5)^2     = 18  +9  +25   

(x-3)^2      + (y+5)^2    = 52                <==== this is a circle centered at 3,-5   with radius = sqrt (52) 

 

Area of a circle = pi r^2 

                         = pi (sqrt (52) )^2   = 52 pi = 163.4 units^2 

 Sep 6, 2024

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