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(No explanation needed, but if you do, THANK YOU SO MUCH! :) )

 

The equation of a circle which has a center at (-5,2) can be written as $Ax^2 + 2y^2 + Bx + Cy = 40$. Let $r$ be the radius of the circle. Find $A + B + C + 4$. 

 

(I tried to do it, and I got $14 + 7 sqrt 2$, but apparently, that is incorrect.)

 

Thank you so much! 

Guest Nov 12, 2018

Best Answer 

 #1
avatar+14543 
+2

Cirle formula  

    (x-h)^2   + (y-k)^2 = r^2       center = h,k

                   ( x+5)^2 + (y-2)^2 =r^2

                   x^2 + 10x   + 25   + y^2 -4y   + 4 = r^2

                  x^2  + y^2 + 10x -4y  = r^2 -29                 Multiply both sides by 2 to get the 2y^2

                 2 x^2 + 2y^2 + 20x - 8y = 2r^2 - 58         and 2^r^2 - 58 = 40     2r^2 = 98   r^2 = 49     r= 7

 

A+B + C +4 = 2 + 20 + (-8) + 4  = 18

 

IF you meant    A+B+C+r     then  =   2+20+(-8) +  7 = 21

ElectricPavlov  Nov 12, 2018
edited by ElectricPavlov  Nov 12, 2018
edited by ElectricPavlov  Nov 12, 2018
 #1
avatar+14543 
+2
Best Answer

Cirle formula  

    (x-h)^2   + (y-k)^2 = r^2       center = h,k

                   ( x+5)^2 + (y-2)^2 =r^2

                   x^2 + 10x   + 25   + y^2 -4y   + 4 = r^2

                  x^2  + y^2 + 10x -4y  = r^2 -29                 Multiply both sides by 2 to get the 2y^2

                 2 x^2 + 2y^2 + 20x - 8y = 2r^2 - 58         and 2^r^2 - 58 = 40     2r^2 = 98   r^2 = 49     r= 7

 

A+B + C +4 = 2 + 20 + (-8) + 4  = 18

 

IF you meant    A+B+C+r     then  =   2+20+(-8) +  7 = 21

ElectricPavlov  Nov 12, 2018
edited by ElectricPavlov  Nov 12, 2018
edited by ElectricPavlov  Nov 12, 2018
 #2
avatar
0

Thank you so much, Electric Pavlov!

 

(I checked your work and saw r = 7, but when you added A, B, C, and r, you put r as 4. I think you meant to put r as 7, so the answer was supposed to be 21.) Thank you anyways, I really appreciate the response. 

 

Sorry,  I just realized that I typed my question wrong! :) But thank you anyways!

Guest Nov 12, 2018
edited by Guest  Nov 12, 2018
edited by Guest  Nov 12, 2018
 #3
avatar+14543 
+2

   I added 4 instead of r   because that is what your posted question asked.  cheeky

ElectricPavlov  Nov 12, 2018

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