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# inequalities

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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