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Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y - 10x + 14y + 88.

 Nov 25, 2022
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Combining like terms and rearranging the equation: x2+8x+y2-8y=88

Then you would complete the square for the x and y: (x+4)2-16+(y-4)2-16=88. You subtract 16 for both to keep the equation the same. Moving then to the left side gives (x+4)2+(y-4)2=120. This is the equation of a circle with a radius of \(\sqrt{120} \).

Then you just find the area using the radius.

Hope this helps!

 Nov 25, 2022

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