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avatar+563 

Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+14x-14y+28

 Jun 24, 2024

Best Answer 

 #2
avatar+129725 
+1

Simplify as

 

x^2 -16x + y^2 + 20y  = 34     complete the square on x, y

 

x^2 -16x + 64 + y^2 + 20y + 100 =  34 + 64 + 100

 

(x - 8)^2  + ( y +10)^2  =  198

 

This is a circle centered at ( 8 , -10)   with r^2 =  198

 

Area =  pi * r^2  =  198 pi

 

cool cool cool

 Jun 25, 2024
 #1
avatar+85 
0

\( x^2+y^2=2x-6y+6+14x-14y+28\)

This is just a circle. i moved the xs and ys to the left and that just moves the circle. the size depends on the constant which is 34. so the area of the circle would be 34pi

 Jun 24, 2024
 #2
avatar+129725 
+1
Best Answer

Simplify as

 

x^2 -16x + y^2 + 20y  = 34     complete the square on x, y

 

x^2 -16x + 64 + y^2 + 20y + 100 =  34 + 64 + 100

 

(x - 8)^2  + ( y +10)^2  =  198

 

This is a circle centered at ( 8 , -10)   with r^2 =  198

 

Area =  pi * r^2  =  198 pi

 

cool cool cool

CPhill Jun 25, 2024

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