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Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y + 13 - 2x + 8y + 15.

 Apr 15, 2022
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x^2 + y^2 <= 4x + 6y + 13 - 2x + 8y + 15

 

Rewrite  as

 

x^2 -2x + y^2 - 14y ≤ 28     complete the square on  x and y

 

x^2 -2x + 1  + y^2 -14y + 49 ≤  28 + 1 + 49

 

(x - 1)^2 + (y - 7)^2 ≤  78

 

This is a  circle  centered at (1, 7)  with a radius^2  of 78

 

The area lies within the circle and   =    78pi  units^2

 

cool cool cool

 Apr 15, 2022

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