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In terms of pi, what is the area of the circle defined by the equation 2x^2+2y^2+10x-6y-18=x^2+y^2+5x-y?

 Jun 27, 2022
 #1
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The area is 47*pi

 Jun 27, 2022
 #2
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Isolate the constant: x2+y2+5x5y=18

 

Rearrange as follows: (x2+5x)+(y25y)=18

 

Add 6.25 to complete the square on x, and add another 6.25 to complete the square on y. 

 

This gives: (x+2.5)2+(y2.5)2=30.5.

 

Note that the constant (30.5) is r2, meaning the area of the circle, in terms of pi, is 30.5π

 Jun 27, 2022

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