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

 Feb 10, 2021
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4x + 6y + 13 + 2x   -2y   simplifies to

 

6x + 4y + 13

 

So

 

x^2 + y^2  ≤  6x + 4y  + 13

 

x^2  -6x  + y^2 -4y  ≤ 13       complete the square on x and  y

 

x^2  - 6x + 9  +  y^2  - 4y + 4 ≤ 13 + 9 + 4

 

(x - 3)^2  + (y - 2)^2  ≤  26

 

This is just the  area  inside  the circle  with a center of  ( 3, 2)   and a radius of  sqrt (26)

 

See here  : https://www.desmos.com/calculator/0c8kf8nfll

 

The area  is    pi (sqrt (26))^2 =    26 pi

 

 

 

cool cool cool

 Feb 10, 2021

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