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Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.

 Feb 12, 2024
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Graph of a Circle: (x - h)^2 + (y - k)^2 = r^2

Circle with center (h, k), radius r. 

 

Move variable terms to one side:

\(x^2-16x+y^2+22y=86\)

Complete the square:

\((x-8)^2-64+(y+11)^2-121=86\)

\((x - 8)^2+(y+11)^2=86+121+64=271=r^2\)

 

The area of the circle is \(\pi{r^2}=271\pi\)

 Feb 12, 2024

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