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Can you help with this?

 

What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?

 Sep 8, 2023
 #1
avatar+126971 
+1

x^2+y^2 - 7 = 4y-14x+2x-6y+3

 

Rearrange as

 

x^2 +12x + y^2 + 2y = 10         complete te square on x,y

 

x^2 + 12x +  36  + y^2 + 2y + 1 =  10 + 36 + 1

 

(x + 6)^2 + ( y + 1)^2  = 47

 

This is a circle centered at ( -6, -1)  with a radius of  sqrt (47)

 

The area of the circle =  pi * r^2  =   pi * ( sqrt 47)^2  =  47 pi

 

cool cool cool

 Sep 8, 2023

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