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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?

 Jan 16, 2019
 #1
avatar+16487 
+3

If you rearrange the equation into the standard form of a circle....you will find r = sqrt(17.5)

 

pi r^2 = area = 17.5 pi

 Jan 16, 2019
edited by Guest  Jan 16, 2019
 #2
avatar+429 
0

this is a more helpful version of EP's solution:

 

rearranging terms, you get 2x^2+10x+2y^2-6y=18. completing the square, you get 2(x + 2.5)^2 + 2(y - 1.5)^2 = 18 + 4.5 + 12.5, or (x + 2.5)^2 + (y - 1.5)^2 = 17.5. Now it is just a matter of multiplying the right side by pi, so it is 35pi/2.

 

HOPE THIS HELPED!

 Jan 16, 2019
 #3
avatar+96439 
+1

2x^2 + 2y^2 + 10x - 6y - 18 = 0?

Divide through by 2  and rearrange

 

x^2 + 5x + y^2 - 3y   =  9       complete the square on x and y

 

x^2 + 5x + 25/4   + y^2 - 3y + 9/4  =   9 + 25/4 + 9/4

 

Simplifying the right side, we have

 

17/2 + 9  =   35/2        this  is r^2

 

So....the area  =   pi (35/2)  =  17.5 pi  units^2

 

 

cool cool cool

 Jan 16, 2019

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