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Help I don't know how to graph circles

 

The equation of a circle in the coordinate plane can be written as $Ax^2 + 2y^2 + Bx + Cy = 50.$ The center of the circle is at $(-5,2)$.  Let $r$ be the radius of the circle. Find $A+B+C+r.$

 Aug 27, 2023
 #1
avatar+128732 
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The center is   (-5, 2)     

 

So we have that

 

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

 

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

 

x^2  + y^2 + 10x   - 4y   =  r^2   - 29      multipy through by 2

 

2x^2 + 2y^2  + 20x  - 8y  = 2r^2  -58

 

A = 2   B   = 20  C  = -8

 

And we  know that

 

2r^2  - 58  = 50       divide through by 2

 

r^2  - 29  = 25

 

r^2  = 54 

 

r =sqrt (54)

 

A + B + C  + r =   2 + 20  - 8  + sqrt (54)  =    14 + sqrt (54)  = 14 + sqrt (9 * 6)  = 14 + 3 sqrt (6)

 

 

cool cool cool

 Aug 27, 2023

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