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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

 

 

and if you could please help me on this

 

What is the value of x if absolute value (x-1)=(x-2)? Express your answer as a common fraction.

 Aug 8, 2020
edited by Guest  Aug 8, 2020
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Step 1)  Place the equation into graphing form:  2x2 + 2y2 + 10x - 6y - 18  =  0

                     divide by 2:                                             x2 + y2 + 5x - 3y - 9  =  0

                     rearrange:                                         x2 + 5x       + y2 - 3y       =  9

                     complete the square:             x2 + 5x + 25/4  +  y2 - 3y + 9/4  =  9 + 25/4 + 9/4

                     simplify:                                                 (x + 5/2)2 + (y - 3/2)2  =  35/2

 

Step 2)  Find the radius:  sqrt(35/2)

 

Step 3)  Find the area:  Area  =  pi ·[ sqrt(35/2) ]2  =  pi · 35/2

 Aug 8, 2020

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