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Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y + 13 - 2x + 8y.

 Feb 12, 2021
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Rearrange  as

 

x^2 - 4x +  2x  +  y^2  - 6y  - 8y   ≤ 13      simplify

 

x^2  -  2x  +  y^2  - 14y  ≤  13       complete  the  square on x and y

 

x^2  - 2x + 1 + y^2  - 14y  + 49   ≤  13 + 1 + 49

 

(x - 1)^2   +  (y  - 7)^2  ≤  63

 

This is a circle centered at  ( 1, 7)    with a radius  of sqrt (63)

 

The inequality tells us that we  only  want to find  the area inside this circle   =  pi  (sqrt (63))^2  =   63 pi  units^2

 

 

cool cool cool

 Feb 12, 2021

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