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# graphing circles

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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

#1
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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
+33727
+3

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