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The graph of (x + 3)^2 + (y - 7)^2 = 16 is reflected over the line y = 2. The new graph is the graph of the equation x^2 + Bx + y^2 + Dy + F = 0 for some constants B, D, and F. Find B + D + F.

 Dec 1, 2020
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The center of the circle  =  ( -3, 7 )

 

When reflected across the line y = 2, the new  center will be  (-3, 2 - 5)  = (-3,-3)

 

The new circle is

 

(x +3)^2  + ( y +3)^2  = 16

 

x^2  + 6x  + 9  + y^2 + 6x + 9   =16

 

x^2  + 6x + y^2  + 6y  + 2  = 0

 

B =  6    D =  6   F  = 2

 

And their sum  =14

 

cool cool cool

 Dec 1, 2020

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