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Find the area of the region satisfying the inequality x^2 + y^2 \(\leq\) 4x + 6y + 13

 Feb 27, 2021
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Rewrite the inequality as

 

x^2 - 4x + y^2 - 6y ≤ 13

 

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

 

(x-2)^2 + (y - 3)^2 ≤ 26

 

This is the area of a circle centred on x = 2, y = 3, with a radius of r = √26.

 

I'll leave you to find the area of a circle with radius r = √26.

 Feb 27, 2021

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