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In terms of $\pi$, what is the area of the circle defined by the equation $2x^2+2y^2+10x-6y-18=0$?

 Apr 12, 2021

Best Answer 

 #1
avatar+33727 
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This is the equation of a circle ......re write in standard form by 'completing the square' for x and y :

 

2 x^2 + 10x       + 2y^2 -6y  - 18 = 0      divide through by 2

x^2 + 5x            + y^2 -3y      = 9          complete the squares

 

(x+2.5)^2              + ( y-1.5)^2     = 9 + 6.25  + 2.25   <======== this equals radius ^2

 

                                                 17.5 = r^2           area of circle = pi r^2        area =   17.5 pi  units2

 Apr 12, 2021
 #1
avatar+33727 
+3
Best Answer

This is the equation of a circle ......re write in standard form by 'completing the square' for x and y :

 

2 x^2 + 10x       + 2y^2 -6y  - 18 = 0      divide through by 2

x^2 + 5x            + y^2 -3y      = 9          complete the squares

 

(x+2.5)^2              + ( y-1.5)^2     = 9 + 6.25  + 2.25   <======== this equals radius ^2

 

                                                 17.5 = r^2           area of circle = pi r^2        area =   17.5 pi  units2

ElectricPavlov Apr 12, 2021

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