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

 May 12, 2024
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1. The equation is simplified to to find the enclosed area.
 

2. The equation is further rewritten in standard form as (x - 8)^2 + (y + 11)^2 = 271, representing a circle centered at (8, -11) with a radius of the square root of 271 units.

 

 3. The area enclosed by the circle is calculated using the formula A = 271π square units.

 

4. Therefore, the area of the region enclosed by the given graph is 271π square units.

 May 12, 2024

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