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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.

 May 10, 2024
 #1
avatar+128796 
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If this  is a  circle  A  must =  2

 

We can  write

 

2 ( x + 5)^2   + 2(y  - 2)^2  = 50 + 50 + 8

 

2 ( x^2 + 10x + 25)  + 2(y^2 - 4y +4)  = 50 + 50 + 8

 

2x^2 + 20x + 50 + 2y^2 - 8y + 8 =  108

 

A =2

B = 20

C = -8

r = sqrt (108)

 

A + B + C + r   =     14 + sqrt (108)

 

cool cool cool

 May 10, 2024

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