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Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y + 18.

 Jul 21, 2021
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x^2 + y^2 <= 4x + 6y + 18.      re-arrange into circle equation form

 

x^2 -4x       +    y^2-6y    <  = 18      complete the square for x and y

 

(x-2)^2       +   (y-3)^2    <  = 18 + 4 + 9      this is a circle with center   2,3   and radius sqrt(31)

 

 

Area of circle with radius   sqrt(31)        <====== can you calculate that?

 Jul 21, 2021

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