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Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y+13 - 2x + 3y + 9.

 Feb 10, 2021
 #1
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This will be the area inside of a circle...first simplify to

 

x^2 -2x       + y^2-9y      = 22       then complete the square for x and y

(x-1)^2       + (y-4.5)^2   = 22 + 1 + 20.25

                                      = 43.25                          43.25 is the radius squared

          

 

area = pi r^2   = 43.25 π

 Feb 10, 2021
 #2
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* * * edited * * *    ( but answer does not change)

x^2 -2x       + y^2-9y     < = 22       then complete the square for x and y

(x-1)^2       + (y-4.5)^2  < = 22 + 1 + 20.25

                                    <  = 43.25                          43.25 is the radius squared

Guest Feb 10, 2021

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