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

 Mar 15, 2024
 #1
avatar+128406 
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Simplify as

 

x^2 - 16x + y^2 + 22y  =  86        complete the squre on x, y

 

x^2  - 16x + 64  + y^2 + 22y + 121  =  86 + 64 + 121

 

(x - 8)^2   + (y + 11)^2   =  271

 

This is a  circle centered at (8, - 11)

 

r^2  = 217

 

Area =  pi * r^2 =    271  pi  ≈ 851.4

 

cool cool cool

 Mar 15, 2024

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